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