Question

The second side of a triangular deck is 3 feet longer than the shortest​ side, and the third side is 3 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 72 ​feet, what are the lengths of the three​ sides?

Answer 1

The length of the shortest​ side is 18 ft

The length of the second side is 21 ft

The length of the third side is 33 ft

Explanation:

Let

x ------> the length of the shortest​ side

y -----> the length of the second side

z ----> the length of the third side

we know that

The perimeter of the deck is

P=x+y+z

P=72 ft

so

72=x+y+z ------> equation A

y=x+3 ------> equation B

z=2x-3 -----> equation C

substitute equation B and equation C in equation A and solve for x

72=x+(x+3)+(2x-3)

72=4x

x=72/4

x=18 ft

Find the value of y

y=18+3=21 ft

Find the value of z

z=2(18)-3=33 ft

therefore

The length of the shortest​ side is 18 ft

The length of the second side is 21 ft

The length of the third side is 33 ft