Solving Quadratics using the Quadratic Equation

Question

The hypotenuse of an isosceles right triangle is 8 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.)

The length of one leg is

the length of the other is

and the length of the hypotenuse is

Answer 1

hypotenuse= h = 8+L where L = Length of the other Legs

h^2 = 2L^2

(8+L)^2 = 2L^2

64 + 16L + L^2 = 2L^2

L^2 -16L -64 = 0

L^2 -16L + 64 = 64+64

(L-8)^2 = 128

L-8 = sqr128

L = 8 +sqr128

L = 8+8sqr2

L = 8(1+sqr2)

L = about 8(2.414)

= about 19.314 cm Long for each of two Legs

h = 8+L = about 27.314 cm = the Hypotenuse

h also = Lsqr2 = about 19.314(1.414) = about 27.314