Question

The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.​ (hint: an isosceles right triangle is a right triangle whose legs are the same​ length.)

Answer 1

Given,
Hypotenuse of an right angle isosceles triangle is 11centimeters longer than the length of each side.
So Let, the sides of the isosceles right angle triangle are x,x, 11+x
In a right angle triangle
hypotenuse^2 = Side ^2 + side ^2
(11+x)^2 = x^2 +x^2
(11+x)^2= 2(x^2)
By solving
x=26.5
So the sides are 26.5,26.5 and 37.5