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?

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

One unique triangle, because those angles add up to 180, and that's how many degrees there are in one triangle.

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