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.

first anwser choice.

step-by-step explanation:

the greater/less or equal to symbol (> or < with the line at the bottom) is a closed/filled in circle.

when multiplying or dividing by a negative on both sides you have to flip the inequality sign. this rule only applies to multiplying or dividing by a negative number in inequality equations. this rule is really important.

-5c + 2 _< _27

subtract from both sides by 2

-5c _< _ 27

divide both sides by -5

c _< _ 5.4

flip the inequality sign

c _> _5.4

the only possible answer that would match the simplified inequality is the first answer choice