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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.

Sagot :

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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.
[tex]x+\frac{1}{2}x+x-12=53 \\ x+\frac{1}{2}x+x=65 \\ 2\frac{1}{2}x=65 \\ \frac{5}{2}x=65 \\ x=65 \times \frac{2}{5} \\ x=13 \times 2 \\ x=\boxed{26} \\ \\ \frac{1}{2}x=\frac{1}{2} \times 26=\boxed{13} \\ \\ x-12=26-12=\boxed{14}[/tex]

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