The perimeter of a quadrilateral (four-sided polygon) is 55 inches. The longest side is four times as long as the shortest side.

Question

The perimeter of a quadrilateral (four-sided polygon) is 55 inches. The longest side is four times as long as the shortest side. The other two sides are equally long and are 3 inches longer than the shortest side. Find the length of all four sides.

 

Answer 1

short side = x

long side = 4x

other sides are each x + 3

Perimeter = sum of all four sides

x + 4x + x+3 + x+3 = 55

7x + 6 = 55

7x = 49

x = 7 4x = 28 x+3 = 10

The lengths of the four sides are 7, 10, 10, and 28.