A triangle has a perimeter of 24 feet. The shortest side is 4 feet shorter than the longest side, and the sum of the shortest and longest sides is equal to twice the length of the other side. What are the lengths of the three sides of this triangle?
A triangle has a perimeter of 24 feet. The shortest side is 4 feet shorter than the longest side, and the sum of the shortest and longest sides is equal to twice the length of the other side. What are the lengths of the three sides of this triangle?
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.