Question

The ratio of the measures of the sides of a triangle is 7:9:12, and its perimeter is 84 inches. Find the measure of each side of the triangle.

Answer 1

To find the measures of each side of the triangle given the ratio of the sides \(7:9:12\) and a perimeter of \(84\) inches, we can follow these steps:

1. **Identify the ratio parts**:
Let the sides of the triangle be represented as \(7x\), \(9x\), and \(12x\), where \(x\) is a common multiplier.

2. **Set up the equation using the perimeter**:
The perimeter of the triangle is the sum of the lengths of its sides:
\[
7x + 9x + 12x = 84
\]

3. **Combine the terms**:
Combine the terms on the left side:
\[
(7 + 9 + 12)x = 84
\]
This simplifies to:
\[
28x = 84
\]

4. **Solve for \(x\)**:
Divide both sides by the coefficient of \(x\):
\[
x = \frac{84}{28} = 3
\]

5. **Calculate the lengths of each side**:
Now substitute \(x\) back into the expressions for each side:
- First side:
\[
7x = 7 \times 3 = 21 \text{ inches}
\]
- Second side:
\[
9x = 9 \times 3 = 27 \text{ inches}
\]
- Third side:
\[
12x = 12 \times 3 = 36 \text{ inches}
\]

6. **Present the measures of each side**:
The measures of the sides of the triangle are:
- First side: \(21\) inches
- Second side: \(27\) inches
- Third side: \(36\) inches

Thus, the sides of the triangle are **21 inches, 27 inches, and 36 inches**.