need help with number 152

[brave grove]

let HB = x, BE = 21-x

[shadow breach]

Try forming equations using Pythagorean theorem

[brave grove]

and HT = EA

[silk crystal]

Just find the area of triangle by heron's formula and double it

You don't need to consider x

Triangle's sides are 21 10 and 17

[silk crystal]

168

[flat yew]

how about this?

the shaded region

[silk crystal]

Which one?

[silk crystal]

I've just taken the ratio of sides

You can solve by x but i prefer this method

155.) 3

the slope will be same so, 2x-y will equal 6 and 2x-y=6 is the equation. 6 because that's the value when we put those coordinates. Now just put y=0

[flat yew]

oh only the shaded area haha but anyway thanks!!!

[flat yew]

i also need help with this one

[silk crystal]

I love geometry

You can send my any no. Of Questions.

[flat yew]

can you help me with number 160?

[silk crystal]

48

[flat yew]

what is the value of r?

[silk crystal]

My answer is right?

I think it is

[flat yew]

my r is fifth root of 2 but it's always error when i plug it

[flat yew]

my r is probably incorrect

[silk crystal]

It's sixth root

Actually you don't need to find r

[flat yew]

yeah i got confused because i did everything mentally

[silk crystal]

You just have to find the ratio

12:24 is 1:2. Because the difference of terms is equal i.e 6th and 12th, 12th and 18th. So they'll have same ratio

[silk crystal]

In the first term the power of r is 0

[silk crystal]

12:24::24:48 so 48 is answer

[flat yew]

bro sorry for my dumb question but why did you use 2 instead of 1?

[flat yew]

is it much simpler if you use 2, because the length of the 2 shorter sides will be a fraction if you'll use 1?

[silk crystal]

You can use any number. I actually didn't choose 2. I chose √2 because I knew by Pythagorean theorem, I'll have a whole number 2 as chord then it'll be easy to calculate the area.

Basically I'm finding the value of x

When the ratio of 2 numbers say 24 and 30 is 4:5, the multiplying factor of 4 and 5 is 6 because if we multiply 6 by 4 and 5 we'll get the original numbers. So , the number 4 here is the number 18 in my question.
In case, we square 24 and 30, we square the multiplying factor too. But here our area was already 1 in ratio and 18 unit² in actuality so we didn't need to multiply by the square of multiplying factor

If you take the radius as √2x , and do the process, you'll understand why I did what I did

[lone tundra]

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