Question

Solve- question help 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?

Answer 1

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.

Answer: 13 ft, 17 ft, 22 ft

Answer 2

shortest side: s

second side: s + 4

third side: 2s - 4

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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

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shortest side: s ⇒ 13 feet

second side: s + 4 ⇒ 13 + 4 = 17 feet

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