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 riangle wh

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Question 435673: 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 riangle whose legs are the same length)
The length of one leg is
The length of the oter leg is
the length of the hypotenuse is
(simplify your answer using radicals as needed)
Found 2 solutions by mananth, ewatrrr:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
x^2+x^2=(x+7)^2
2x^2=x^2+14x+49
x^2-14x-49=0
Find the roots of the equation by quadratic formula
a= 1 b= -14 c= -49
b^2-4ac=196+196
b^2-4ac=392 sqrt(392)=19.8


x1=(14+19.8)/2
x1=16.9
x2=(14-19.8)/2
x2= -2.9
Ignore negative value
The leg is 16.9 cm
Hypotenuse = 23.9 cm

Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!


Hi

the hypotenuse of an isosceles right triangle is 7 centimeters longer than either of its legs. 

Let x, x and (x+7)represent the lengths of each leg and the hypoenuse respectively

using the Pythagorean Theorem to find the lengths of the sides

    x^2 + x^2 = (x+7)^2

     2x^2 = x^2 + 14x + 49

      x^2 - 14x-49 = 0

 

 

 

 

 

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