a = the first side
b = the second side
c = the third side
P = the perimeter
a = 2 b - 5
c = a + 2 = 2 b - 5 + 2 = 2 b - 3
P = a + b + c = 47
a + b + c = 47
2 b - 5 + b + 2 b - 3 = 47
5 b - 8 = 47 Add 8 to both sides
5 b - 8 + 8 = 47 + 8
5 b = 55 Divide both sides by 5
b = 11 km
a = 2 b - 5 = 2 * 11 - 5 = 22 - 5 = 17 km
c = a + 2 = 19 km
P = a + b + c = 17 + 11 + 19 = 47 km
The perimeter of a triangle is 47 km. the first side is 5 km shorter than twice the second. the third side is 2 km longer than the first. find the length of each side.
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