Question

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

Answer 1

`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)`

Answer 2

`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"`