2500.21 – Finding Sides of a Triangle

The lengths of the sides of this particular triangle are consecutive integers. The length of the shortest side is 30 percent of the triangle’s total perimeter. Find the length of the three sides.

Solution

The sides are consecutive, so let us say they are nn, n+1n+1, and n+2n+2. Here's how to solve for the shortest side, nn.

n=0.3(n+(n+1)+(n+2))=0.3(3n+3)=0.9n+0.9.1n=0.9n=9.\begin{aligned}n &= 0.3(n + (n+1) + (n+2))\\&= 0.3(3n+3) \\&= 0.9n + 0.9 \\.1 n &= 0.9 \\n &= 9.\end{aligned}

The sides are nine, ten, and eleven each. The total perimeter is 30.