the perimeter of a triangle is 83inches. the longest side is three times the length of the shortest side and 17inches more than one-half the sum of the other two sides. use a system of equations to find the length of each side.

Question

anonymous · Answer

a=3b
a = 0.5(b+c) + 17
a + b + c = 83
so 3b = 0.5b + 0.5c + 17
and 3b + b + c  = 83
2.5b = 0.5c + 17
4b  = -c + 83
5b = c + 34
add
9b = 117
b = 13
so a = 3*13 = 39
and c = 83-39-13 = 31
lengths of sides
= 13,31 and 39