Question

The first side of a triangle of 8 in shorter than the second side. The third side is 4 times as long as the first side. The perimeter is 26 in. Find the length of the longest side?

Answer 1

The longest side is 12 inches long.

Explanation:

Let `x` be the first side.

Since `x` is 8 in. shorter than the second side, we know that we'd need to add 8 to `x` to get the length of the second side. So the second side is `x+8`. (Think, if the first side is 2 inches and it is 8 inches shorter than the second side, the second side must be 10 inches, so this works.)

The third side is 4 times the length of the first side, so the third side is `4x`.

Perimeter is the sum of the sides, so: `(x) + (x+8) + 4x=6x+8`

We also know the perimeter is 26, so we have:

`6x+8=26`

subtract 8:

`6x=18`

divide:

`x=3`.

The three sides have length: 3, 11, and 12.

The longest side is 12 inches long.