Problema Solution
the hypotenuse of an isosceles right triangle is 9cm longer than either of is legs. find the EXACT length of each side
Answer provided by our tutors
let
a = the length of each of the legs, a>0
b = the length of the hypotenuse, b>0
the hypotenuse of an isosceles right triangle is 9 cm longer than either of is legs
b = 9 + a
using the Pythagorean Theorem we can write
a^2 + a^2 = b^2
2a^2 = b^2
plug b = 9 + a into the last equation
2a^2 = (9 + a)^2
by solving we find
a = 9 + 9√2
click here to see the step by step solution of the equation
b = 9 + 9 + 9√2
b = 18 + 9√2
the EXACT length of each side is: the hypotenuse is 18 + 9√2 cm and each of the legs is 9 + 9√2 cm.