Question

The legs of the isosceles right triangle each measure 14 inches. What is the length of the hypotenuse?

Answer 1

`14sqrt2`

Explanation:

First, recognize that an isosceles triangle means two sides are the same. Another keyword here is 'right triangle'. This suggests that it is possible to use the Pythagorean theorem (`a^2 + b^2 = c^2`).

Using this formula, we can easily find the length of the hypotenuse.

In the Pythagorean theorem, `a` and `b` are always the legs of the right triangle, which are the two sides that make up the right angle. The variable `c` is always the hypotenuse. Since we already have both legs, (`14`) all we have to do is substitute.

`14^2 + 14^2 = c^2`
`14^2 = 196`
`196 + 196 = c^2 = 392`
`c = sqrt392`

We can simplify this root by splitting it into its factors.

`392 = 2 * 2 * 2 * 7 * 7`
`sprt392 = sqrt(2 * 2 * 2 * 7 * 7) = sqrt(2*2) * sqrt(2) * sqrt(7*7)`
`=2*7*sqrt2 = 14sqrt2`

Final answer:

`14sqrt2`