Question

A vacant city lot is being turned into a neighborhood garden. the neighbors want to fence in a triangular section of the lot and plant flowers there. the longest side of the triangular section is 77 feet shorter than twice the shortest side. the third side is 22 feet longer than the shortest side. the perimeter is 5959 feet. how long is each​ side?

Answer 1

Let x represent the length of the shortest side. Then the longest side is

... 2x -7 . . . . . . 7 ft shorter than twice the shortest side

and the 3rd side is

... x +2 . . . . . . 2 ft longer than the shortest side.

The perimeter is the sum of the side lengths,

... x + (2x -7) + (x +2) = 59 . . . . . the given perimeter length

... 4x -5 = 59 . . . . collect terms

... 4x = 64 . . . . . . add 5

... x = 16 . . . . . . . . divide by 4

Then the other sides are

... 2×16 - 7 = 25 . . . . . longest side

... 16 +2 = 18 . . . . . . . . third side

The side lengths are 16 ft, 18 ft, and 25 ft.