Atrapezoid has a perimeter of 117cm. the two shortest sides have the same length. the third side is 12cm longer than one short side. the final side is 9cm less than three times one short side. how long is each side of the trapezoid?

First, make an equation system for the problem

An equation for "A trapezoid has a perimeter of 117cm" is
⇒ s₁ + s₂ + s₃ + s₄ = 117
    "two shortest side is the same"
    2s₁ + s₃ + s₄ = 117

An equation for "the third side is 12cm longer than one short side"
⇒ s₃ = s₁ + 12

An equation for "the final side is 9cm less than three times one short side"
⇒ s₄ = 3s₁ - 9

Second, solve the problem by subtitution method.
Subtitute s₃ with s₁+12 and subtitute s₄ with 3s₁-9
2s₁ + s₃ + s₄ = 117
2s₁ + (s₁ + 12) + (3s₁ - 9) = 117
6s₁ + 3 = 117
6s₁ = 117 - 3
6s₁ = 114
  s₁ = 114/6
  s₁ = 19
The length of two shortest sides each is 19 cm

Find the third side
s₃ = s₁ + 12
s₃ = 19 + 12
s₃ = 31
The length of third side is 31 cm

Find the fourth side
s₄ = 3s₁ - 9
s₄ = 3(19) - 9
s₄ = 57 - 9
s₄ = 48
The length of fourth side is 48 cm

ANSWER:
The lengths of the sides are 19 cm, 19 cm, 31 cm + 48 cm