Question

If the hypotenuse of a triangle is 30 inches and one of the legs is 10 in, how long is the other leg?

Answer 1

The leg is `20sqrt2`

Explanation:

We'll solve this using the Pythagorean Theorem.

`a^2 + b^2 = c^2`
where `a` and `b` are the length of the legs , and `c` is the length of the hypotenuse.

Let's plug in the values in the question:
`a^2 + b^2 = c^2`
`10^2 + b^2 = 30^2`
`100 + b^2 =900`
`b^2 = 800`
`b=sqrt800`

Now simplify `sqrt800` to find the exact length:
`sqrt800=sqrt(2×2^2×(2×5)^2)=2×2×5×sqrt2=20sqrt2`

The length of the side is `20sqrt2`