An isosceles right triangle has legs that are each 4cm. What is the length of the hypotenuse?

2 Answers
Nov 14, 2015

c = sqrt(32)

Explanation:

We will use the Pythagorean Theorem for this problem.

We know that each leg is 4cm. We can plug those in for a and b, to find our hypotenuse, c.

4^2 + 4^2 = c^2
16 + 16 = c^2
32 = c^2
c = sqrt(32)

Nov 14, 2015

4sqrt(2)"cm"

Explanation:

By the Pythagorean theorem, the square of the hypotenuse of a right triangle is equal to the sum of the squares of it's legs. That is, for a right triangle with legs a and b and hypotenuse c
a^2 + b^2 = c^2

In this case, we have a = b = 4"cm", thus

c^2 = (4"cm")^2 + (4"cm")^2 = 32"cm"^2

=> c = sqrt(32"cm"^2) = sqrt(16*2)"cm" = 4sqrt(2)"cm"