Several geometry questions.

[trim egret]

First one. Find DM + DN in triangle ABC if AB=BC=10 and area of ABC is 50.
I drew the height BK, we know that AB is 10. lets say height is "h" and AK is x. We know that in isosceles triangle height is same as median and bisector. So AK = KC. area of ABC is 1/2 * 2x * h = 50 from here xh=50
also we know that hˆ2 + xˆ2 = 10. But there is no solution. What am i doing wrong

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[worthy nebula]

Hmm

I don't quite understand your method

Ah, I see.

[worthy nebula]

$h^2+x^2=10^2$, not $h^2+x^2=10$

[graceful quarry]

Kocher

[worthy nebula]

Basically, you forgot to square the 10 when doing the pythagorean theorem

Then this leads you to a singular solution

[trim egret]

oh my god bro im so sorry. my brain is not braining

im tired of math

[worthy nebula]

It's fine

I've made worse mistakes

[trim egret]

but i started with right method yeah?

[worthy nebula]

Yes

Frankly, I don't see how it would help with the question

[trim egret]

so im getting -5sqrt(2) and 5sqrt(2) i can pick up only positive one

then x = y ?

[worthy nebula]

Wait forget I said that

It helps a ton

[worthy nebula]

Yes

Spoiler: ||ABC has a right angle at B||

Ok one more thing

[trim egret]

yeah because x and h are equal so angles are 45 and 45. and BK is bisector of angle B therefore 45 * 2 = 90

[worthy nebula]

Since there is no given information on MD and DN, we can assume WLOG (without loss of generality) that D is colinear to B

[worthy nebula]

Yes

[trim egret]

and D is 90 too

[worthy nebula]

Unless there is given information which you have not provided?

[worthy nebula]

Yes

[worthy nebula]

Hence this

[trim egret]

bro i have no idea what to do

[trim egret]

@worthy nebula you here

[worthy nebula]

Oh shit

I was out sorry

[worthy nebula]

Try what I said earlier

[worthy nebula]

^ (I meant to say that D is the foot of the perpendicular bisector of AC)

[trim egret]

i did not get it im sorry bro

wdym

[worthy nebula]

Uh

[trim egret]

i really got no idea

[worthy nebula]

You know what

Take a break

I gotta take one too

[trim egret]

i know but i cant. Next week i got an exam. Not school exam but government exam. So not passing it wont get me into any uni. Thats why

yeah i got it man

@worthy nebula

from here i get a = 5. and MD = DN. so 2 * 5 = 10

[trim egret]

+close

[sage panther]

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[sage panther]

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