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