Question

The consecutive sides of a quadrilateral have lengths (17 - x), (24 - x), (40 - 3x) and (x + 1). If the quadrilateral is a parrelleogram, whats is its perimeter .
Please include work.

Answer 1

The opposite sides of a parallelogram are congruent, so 17-x = 40-3x, and 24-x = x+1. let's start with the first pair: 17-x=40-3x. start by adding 3x to both sides to get 17+2x=40. then subtract 17 from both sides to get 2x = 23, so x = 11.5. so the length of these two sides is 17-11.5 and 40-3(11.5), which is 5.5. since 24-x=x+1, and we know x=11.5, then the length of these two sides (24-x and x+1) is 12.5. the perimeter of the quadrilateral is 5.5 + 5.5 + 12.5 + 12.5, which is 36.