The perimeter of a quadrilateral (four-sided polygon) is 58 inches. The longest side is three times as long as the shortest side. The other two sides are equally long and are 5 inches longer than the shortest side. Find the length of all four sides.

Step-by-step explanation:

From an algebraic perspective.

polygon had four sides.

perimeter (sides added together) = 58inches.

longest side + shortest side + (shortest side + 5) + (shortest side + 5) = 58

let shortest side be s

3s + s + (s + 5) + (s + 5) = 58

4s + (s + 5) + (s + 5) = 58

6s + 10 = 58

6s = 58 - 10

6s = 48

s = 48 : 6

s = 8

Therefore,

longest side = 3 (shortest side)

longest side = 3 (8)

longest side = 24 inches

shortest side = 8 inches

the other two sides are equal

side = shortest side + 5

side = 8 + 5

side = 13 inches

*To confirm answer

add all sides together to get back the perimeter.

longest side + shortest side + side + side = perimeter

24 + 8 + 13 + 13 = 58