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In the figure below, GRAH  is a rectangle, RA = 7 , and GA = 10. Determine AH.


[asy] size(4cm);void mra(pair u, pair v, pair w, real r){ draw(v+(u-v)/length(u-v)*r--v+(u-v)/length(u-v)*r+(w-v)/length(w-v)*r--v+(w-v)/length(w-v)*r);} pair g=(0,7); pair h=(0,0); pair a=(sqrt(51),0); pair r=g+a;dot(g); dot(r); dot(a); dot(h);label(


PS. Even though I saw a post on this before, I tried their solution and it didn't work.

 Apr 1, 2019

Alright, so first set up the equation a^2+b^2=c^2

In this equation AR equals a, so put 7 in for a. GA equals c, so put 10 in for c.

You get 7^2+b^2=10^2

From that you get 49+b^2=100

Minus 49 from both sides to get b^2=51

We know that the square root of 51 will be an irational number, so GR is the square root of 51.

You can solve it from there.

 Apr 1, 2019

Lol you gave me the answer! It was sqrt51 but thank you for helping me!

SoulSlayer615  Apr 1, 2019

Thats what i mean by "solve from there"

 Apr 1, 2019

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