Another One Triangle | Mathematics | Page 1

fierce idol Aug 11, 2024, 10:16 AM

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Area of Triangle

wet thunderBOT Aug 11, 2024, 10:16 AM

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restive ocean Aug 11, 2024, 10:23 AM

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Yo

cerulean sky Aug 11, 2024, 10:24 AM

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This problem already have been in problem board, but cant find it, so, i gonna tell solution twice

fierce idol Aug 11, 2024, 10:25 AM

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You could say the base is 8 and say the height is 1?

cerulean sky Aug 11, 2024, 10:26 AM

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fierce idol Area of Triangle

restive ocean Aug 11, 2024, 10:27 AM

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so like you guys only chat regarding the problem?

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and like nothing else?

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(srry, just wondering)

fierce idol Aug 11, 2024, 10:27 AM

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restive ocean so like you guys only chat regarding the problem?

What do you mean?

cerulean sky Aug 11, 2024, 10:28 AM

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restive ocean so like you guys only chat regarding the problem?

Its a problem solving lounge,so, we solve problems

fierce idol Aug 11, 2024, 10:28 AM

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cerulean sky

How can you assume it’s 2 though

cerulean sky Aug 11, 2024, 10:28 AM

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Trapezoid

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For any trapezoid:

fierce idol Aug 11, 2024, 10:30 AM

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Damn thanks

cerulean sky Aug 11, 2024, 10:30 AM

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No problem

fierce idol Aug 11, 2024, 10:38 AM

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cerulean sky No problem

So what are the side lengths since it has to be divided by 2 to make 12?

cerulean sky Aug 11, 2024, 10:39 AM

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Its just areas ratio

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Side length could be any

fierce idol Aug 11, 2024, 10:41 AM

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So for my working out what would l do?

cerulean sky Aug 11, 2024, 10:41 AM

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What u don’t understand?

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Why quadrilateral is trapezoid?

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Or areas ratio?

fierce idol Aug 11, 2024, 10:42 AM

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I don’t really understand how the trapezoid works

cerulean sky Aug 11, 2024, 10:42 AM

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Ok

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So, trapezoid is special type of quadrilateral with pair of parallel sides

fierce idol Aug 11, 2024, 10:43 AM

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Yes

cerulean sky Aug 11, 2024, 10:43 AM

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And now some important lemma:

cerulean sky Aug 11, 2024, 10:44 AM

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fierce idol Area of Triangle

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Do you now it?

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S-area

fierce idol Aug 11, 2024, 10:45 AM

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Is that a and b or 9 and 6?

cerulean sky Aug 11, 2024, 10:45 AM

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a and b

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So, u know triangle area formula with base an height?

fierce idol Aug 11, 2024, 10:46 AM

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Yeh 1/2bh

cerulean sky Aug 11, 2024, 10:47 AM

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Nice, now apply it to these two triangle on picture, knowing that they have same height

cerulean sky Aug 11, 2024, 10:48 AM

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fierce idol Area of Triangle

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Like this

fierce idol Aug 11, 2024, 10:48 AM

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Yes

cerulean sky Aug 11, 2024, 10:49 AM

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Alright, now sorry but one more lemma

fierce idol Aug 11, 2024, 10:49 AM

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Alright appreciate the teachings

cerulean sky Aug 11, 2024, 10:51 AM

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fierce idol Aug 11, 2024, 10:51 AM

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a=c+d

cerulean sky Aug 11, 2024, 10:51 AM

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No, a and b are parallel lines

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c and b are segments

fierce idol Aug 11, 2024, 10:51 AM

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Oh mb

cerulean sky Aug 11, 2024, 10:52 AM

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Just like in previous one h is common due to a//b

fierce idol Aug 11, 2024, 10:52 AM

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H is the same for c and d

cerulean sky Aug 11, 2024, 10:52 AM

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Yes

fierce idol Aug 11, 2024, 10:53 AM

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I don’t want to sound like a dick but how does this relate to the question?

cerulean sky Aug 11, 2024, 10:53 AM

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Now lets look on trapezoid:

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According to our lemma black area=red area

fierce idol Aug 11, 2024, 10:55 AM

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Yes

cerulean sky Aug 11, 2024, 10:55 AM

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On now cut common part and get this:

cerulean sky Aug 11, 2024, 10:56 AM

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fierce idol Area of Triangle

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So, red area=black area

fierce idol Aug 11, 2024, 10:56 AM

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Oh and BC area is AD area

cerulean sky Aug 11, 2024, 10:57 AM

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cerulean sky

And this is an important sign of trapezoid:

fierce idol Aug 11, 2024, 10:57 AM

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Are all areas equal on there or just opposing sides

cerulean sky Aug 11, 2024, 10:58 AM

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cerulean sky

Only for this two triangles

fierce idol Aug 11, 2024, 10:58 AM

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Oh ok thanks l understand that bit what about the larger triangle now?

cerulean sky Aug 11, 2024, 10:58 AM

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In your problem we have 4 and 4 so, this quadrilateral is trapezoid

cerulean sky Aug 11, 2024, 10:59 AM

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cerulean sky

Now using this fact and first lemma we get this

fierce idol Aug 11, 2024, 10:59 AM

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Here

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Are they both 2s due to the trapezoid rule

cerulean sky Aug 11, 2024, 11:00 AM

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fierce idol Area of Triangle

cerulean sky Aug 11, 2024, 11:00 AM

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fierce idol Here

Yes

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If you mean smaller

fierce idol Aug 11, 2024, 11:02 AM

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Nice now what’s the rule for the larger triangle

cerulean sky Aug 11, 2024, 11:02 AM

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cerulean sky

According to the first lemma if a=b S1=S2

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fierce idol Aug 11, 2024, 11:06 AM

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So a/b is 1/2

cerulean sky Aug 11, 2024, 11:07 AM

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Just similarity, according to the first lemma a/b=1/2 and using that BC//AD we notice two similar triangles XCB and XAD with ratio 1/3 and second pair of similar triangles: CBintersection point and AD intersectionpoint and knowing that BC=1/3AD we get 12

fierce idol Aug 11, 2024, 11:08 AM

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How did you get XAD on there where’s the D?

cerulean sky Aug 11, 2024, 11:08 AM

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Picture cut

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4th vertex

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Of trapezoid

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So, you got it?

fierce idol Aug 11, 2024, 11:13 AM

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Not really yet

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How old are you if you don’t mind me asking?

cerulean sky Aug 11, 2024, 11:14 AM

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I dont mind, im 16

fierce idol Aug 11, 2024, 11:14 AM

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Oh ok ur quite smart for a 16 year old

cerulean sky Aug 11, 2024, 11:15 AM

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Huh, thanks, but in my country im literally a pathetic geometry solver

fierce idol Aug 11, 2024, 11:16 AM

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your smart just checking the height of the triangle is 8 and the base is 6 right?

cerulean sky Aug 11, 2024, 11:18 AM

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No, there cant be any proper data about segments length, this is another type of problems, you need to count areal and ratios

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I told u lemmas for solving this problem and u dont need something more to solve it

fierce idol Aug 11, 2024, 11:20 AM

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cerulean sky

What does that mean for the bigger triangle

cerulean sky Aug 11, 2024, 11:21 AM

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This mean that AD=3BC

fierce idol Aug 11, 2024, 11:21 AM

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So what’s the total working for the whole triangle just to make sure ik what I’m dojng

cerulean sky Aug 11, 2024, 11:24 AM

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Using first lemma Sapd=3Sabp=12

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2+2+8+12=24

fierce idol Aug 11, 2024, 11:25 AM

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cerulean sky

What does that letter at the bottom of the fraction?

cerulean sky Aug 11, 2024, 11:25 AM

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P

fierce idol Aug 11, 2024, 11:25 AM

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Next to P

cerulean sky Aug 11, 2024, 11:25 AM

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A

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Or B

fierce idol Aug 11, 2024, 11:26 AM

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BP/PA?

cerulean sky Aug 11, 2024, 11:26 AM

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BP/PD

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Still don’t get it?

fierce idol Aug 11, 2024, 11:28 AM

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BP/PD=BC/AD?

cerulean sky Aug 11, 2024, 11:29 AM

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Yes

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Due to similarity of PBC and PDA

fierce idol Aug 11, 2024, 11:32 AM

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I’ve done that

cerulean sky Aug 11, 2024, 11:32 AM

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Yes

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And equals to 1/3

fierce idol Aug 11, 2024, 11:32 AM

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What equals to 1/3

cerulean sky Aug 11, 2024, 11:33 AM

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BC/AD

fierce idol Aug 11, 2024, 11:33 AM

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1/3 of triangle right

cerulean sky Aug 11, 2024, 11:33 AM

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Just altitude

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SBPA=1/3SPDA=>SPDA=12

fierce idol Aug 11, 2024, 11:34 AM

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Thanks for the help bro your a real one

cerulean sky Aug 11, 2024, 11:36 AM

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No problem

fierce idol Aug 11, 2024, 11:36 AM

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Have a good night

cerulean sky Aug 11, 2024, 11:46 AM

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Thanks, but its day in my time zone

storm plume Aug 11, 2024, 1:37 PM

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.close

#Another One Triangle