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.