Question

The height of an isosceles triangle is 6 and the base is 12. What is its perimeter?

Answer 1

`12sqrt2+12`

Explanation:

Draw a picture. The base with length `12` will be bisected by the height, since this is an isosceles triangle. That means that the height is `6` and the base is split into two sections with length `6`.

This means we have a right triangle with legs of `6` and `6`, and the hypotenuse is one of the unknown sides of the triangle.

We can use the Pythagorean Theorem to determine that the missing side is `6sqrt2`. Since the triangle is isosceles, we know that the other missing side is also `6sqrt2`.

In order to find the perimeter of the triangle, we add its side lengths.
`6sqrt2+6sqrt2+12=color(red)(12sqrt2+12`