the shortest side of a triangle is 7 inches shorter than the longest side. The middle side is twice as long as the short side. Find the length of all three sides if the perimeter is 31 inches.

Question

anonymous · Answer

longest side: L
shortest side: L - 7
middle side: 2(L - 7)
L + (L-7) + 2(L - 7) = 31
L + L - 7 + 2L - 14 = 31
4L - 21 = 31
4L = 52
L = 13
CHECK:
Longest side: 13
Shortest side: 13 - 7 = 6
Middle side: 2(13 - 7) = 2(6) = 12
13 + 12 + 6 =  31