the triangle is composed of 3 sides; we'll call them a, b, and c.

the perimeter being 24 feet means: 24 = a + b + c

the shortest side (we'll call that a) is 4 feet shorter than the longest side (b). therefore, a = b - 4.

the sum of the shortest side (a, or b - 4) and the longest side (b) equals twice the length of the other side, c. therefore: 2c = b + b - 4 or 2c = 2b - 4 or c = b - 2

therefore, 24 = (b - 4) + b + (b - 2)

or 24 = 3b - 6

or 30 = 3b

or b = 10.

therefore, the longest side is 10. the shortest side is 10 - 4, or 6. and the middle side is 10 - 2, or 8.

10, 8, 6.