Question

One side of a triangle is half the longest side.The thirds side is 12 feet less than the longest side. The perimeter is 53 feet. Find all three sides.

Answer 1

the longest side = x
the second side is half the longest side = (1/2)x
the third side is 12 feet less than the longest side = x-12

The perimeter (the sum of all sides) is 53.

`x+(1)/(2)x+x-12=53 \\ x+(1)/(2)x+x=65 \\ 2(1)/(2)x=65 \\ (5)/(2)x=65 \\ x=65 * (2)/(5) \\ x=13 * 2 \\ x=\boxed{26} \\ \\ (1)/(2)x=(1)/(2) * 26=\boxed{13} \\ \\ x-12=26-12=\boxed{14}`

The lengths of the sides are 13, 14 and 26 feet.