Question

The length of the sides of a triangle are three consecutive odd numbers. The shortest side is 20% of the perimeter. What percentage of the perimeter is the largest side?

Answer 1

To calculate the largest side as a percentage of the perimeter of a triangle with sides of consecutive odd numbers, where the shortest side is 20% of the perimeter, set up an equation for the sides, solve for x, and then find the percentage for the largest side.

Step-by-step explanation:

The question asks us to find the percentage of the perimeter that the largest side of a triangle represents, given that the sides are three consecutive odd numbers and the shortest side is 20% of the perimeter. To solve this, let the sides of the triangle be x, x+2, and x+4, where x is an odd number and the smallest side. Since the shortest side is 20% of the perimeter, x = 0.20(x + x+2 + x+4). Solving this equation gives us x. Then, we find the largest side, x+4, and express it as a percentage of the total perimeter by the formula (largest side/perimeter) × 100.

Steps:

1. Set up the equation: x = 0.20(x + x+2 + x+4).
2. Solve for x to find the lengths of the sides.
3. The largest side is x+4; calculate the perimeter.
4. Find the percentage of the perimeter: (x+4)/(3x+6) × 100.