Question

A triangle has two sides equal in length and a third side 5 inches longer than half the length of each of the other two sides. If the perimeter of the triangle is 50 inches, how long is each side?

Answer 1

The equal sides have length `18` and the third has length `14`

Explanation:

Let `x` represent the length of the equal sides. Then the third side has length `x/2+5`.
We know that the perimeter, that is, the sum of the side lengths, is `50`. Thus

`x + x + (x/2+5) = 50`

Combining like terms and subtracting `5` gives us
`5/2x = 45`

Then we multiply by `2/5` to obtain
`x = 18`

Thus the triangle has two sides of length `18` and one of length `18/2+5 = 14`.