SOLUTION: The hypotenuse of an isosceles right triangle is 7 centimeters longer than either of its legs. Find the exact length of each side(an isosceles right triangle is a right triangle w

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Question 436153: The hypotenuse of an isosceles right triangle is 7 centimeters longer than either of its legs. Find the exact length of each side(an isosceles right triangle is a right triangle whose legs are the sae length.)
Find the length of one leg?
Find the length of the other leg?
Find the length of the hypotenuse?
(Simplfy your answer using radicals as needed.)
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
one leg x cm
other leg = x cm
hypotenuse = x+7
x^2+x^2=(x+7)^2
2x^2=x^2+14x+49
x^2-14x-49=0
Solve by quadratic formula
a= 1 b= -14 c= -49

b^2-4ac=196+196
b^2-4ac=392==> sqrt( 392 )=19.8
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=(14+19.8)/ 2
x1= 16.9
x2=(14-19.8)/2
x2= -2.9
Ignore negative value
The legs are 16.9 cm
Hypotenuse = 23.9 cm