Question

The second side of a triangular deck is 4 feet longer than the shortest side, and the third side is 4 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 64 feet, what are the lengths of the three sides?

Answer 1

We don’t know the value of the shorter side, so we will categorize it as x. Side 2 is just 4 feet longer than x, so we would add 4 on to it. Side 3 has double the x, so we would multiply it be 2 for 2x, and subtract the 4 feet from it.

Side 1: x
Side 2: x + 4
Side 3: 2x - 4

If the perimeter is 64 feet, then all of the sides have to add up to it. Therefore, first we add all of the side lengths up:

x + x + 4 + 2x - 4 = 4x.

Now we put 4x, the amount of all these sides added up, equal to the perimeter of 64.

4x = 64. Divide both sides by 4 to get x by itself.
x = 16.

Now that we know x is 16, we will substitute it in for all the side lengths’ equations.

We know that Side 1 was just x, so that will be 16. Since Side 2 was 4 more than x, we’d do 16 + 4 = 20. We substitute 16 in for x in Side 3’s equation: 2(16) - 4 = 32 - 4 = 28.

Therefore, the final lengths of all the sides are:

Side 1: 16
Side 2: 20
Side 3: 28