The second side of a triangular deck is 44 feet longer than the shortest side, and the third side is 44 feet shorter than twice the length of the shortest side. if the perimeter of the deck is 5656 feet, what are the lengths of the three sides?

First, write an equation system based on the problem

For an instance, s₁ is the shortest side, s₂ is the second side, and s₃ is the third side.

"The second side is 44 feet longer than the shortest side" could be written as

⇒ s₂ = s₁ + 44 (first equation)

"The third side is 44 feet shorter than twice the length of the shortest side" could be written as

⇒ s₃ = 2s₁ - 44 (second equation)

"The perimeter is 5656" could be written as

⇒ s₁ + s₂ + s₃ = 5,656 (third equation)

Second, work and solve the equation system

Based on the first and second equations, work on third equation by changing s₂ and s₃ into the term of s₁

s₁ + s₂ + s₃ = 5,656

s₁ + s₁ + 44 + 2s₁ - 44 = 5,656

4s₁ = 5,656

s₁ = 5,656/4

s₁ = 1,414

The shortest side is 1,414 feet long.

Using the first equation, find s₂

s₂ = s₁ + 44

s₂ = 1,414 + 44

s₂ = 1,458

The second side is 1,458 feet long.

Using the second equation, find s₃

s₃ = 2s₁ - 44

s₃ = 2 (1,414) - 44

s₃ = 2,828 - 44

s₃ = 2,784

The third side is 2,784 feet long.

The dimension of the three sides are 1,414 feet, 1,458 feet, 2,784 feet.