Solve- 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 52 feet, what are the lengths of the three sides?

All side lengths are given in terms of the shortest side, so let x = length of the shortest side.

Shortest side = x

Second side = x + 4

Third side = 2x - 4

perimeter = shortest side + second side + third side

x + x + 4 + 2x - 4 = 52

4x = 52

x = 13

The shortest side is x, so it is 13 ft long.

x + 4 = 13 + 4 = 17

The second side is 17 ft long.

2x - 4 = 2(13) - 4 = 26 - 4 = 22

The third side is 22 ft long.

13 ft, 17 ft, 22 ft

shortest side: s

second side: s + 4

third side: 2s - 4

Make the sum of all the side lengths equal 52 feet.

s + (s + 4) + (2s - 4) = 52

Combine like terms.

4s = 52

Divide both sides by 4.

s = 13

shortest side: s ⇒ 13 feet

second side: s + 4 ⇒ 13 + 4 = 17 feet

third side: 2s - 4 ⇒ 2(13) - 4 = 22 feet