Question

The second side of a triangular deck is 6 feet longer than the shortest side and a third side that is 6 feet shorter than twice the length of the shortest side. if the perimeter of the deck is 80 feet, what are the lengths of the three sides?

Answer 1

Answers:

shortest side = 20 feet

medium side = 26 feet

longest side = 34 feet

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Explanation:

x = first side

y = second side

z = third side

Assume x < y < z

y = x+6 since the second side is 6 ft longer than the shortest (first) side

z = 2x-6 because "third side that is 6 feet shorter than twice the length of the shortest side"

P = 80 is the perimeter

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x+y+z = P

x+x+6+z = P .... plug in y = x+6

2x+6+2x-6 = P ... plug in z = 2x-6

4x = P

4x = 80 ... plug in P = 80

x = 80/4 ... divide both sides by 4

x = 20

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first side = x = 20 feet

second side = y = x+6 = 20+6 = 26 feet

third side = z = 2x-6 = 2*20-6 = 34 feet

So,

x = 20, y = 26, z = 34

are the three side lengths

x+y+z = 20+26+34 = 80

and the three side lengths add to 80, so the answer checks out