Question

The second side of a triangular deck is 5ft longer than the shortest side and the third side is 5 fry shorter than twice the length of the shortest side . If the perimeter of the deck is 64ft what are the lengths of all three sides?

Answer 1

We let x be the length of the shortest side of the triangle. If the second side of the triangular deck is 5 ft longer than the shortest side, this can be represented as x + 5. For the third side, it has a length of 5 ft shorter than twice the length of the shortest side. This can be represented as 2x - 5. Given that we have a total perimeter of 64 ft, the sum of the length of the sides must be equal to this. We have

`x+(x+5)+(2x-5)=64`

Solve for x, we get

`\begin{gathered} 4x=64 \\ x=16 \end{gathered}`

Hence, the length of the triangle are:

Shortest side = 16 ft

Second side = 16 ft + 5ft = 21 ft

Third side = 2(16ft) - 5 ft = 27 ft