Question

The ratio of the measures of the sides of a triangle is 3:4:6, and its perimeter is 104 feet. Find the measure of each side of the triangle.

Answer 1

To find the measures of the sides of the triangle, we first denote the lengths of the sides in accordance with the given ratio 3:4:6. Let:

- \( 3x \) be the length of the first side,
- \( 4x \) be the length of the second side,
- \( 6x \) be the length of the third side.

The perimeter of the triangle is the sum of all its sides. Thus, we have:

\[
3x + 4x + 6x = 104 \, \text{feet}
\]

Combining the terms on the left side:

\[
13x = 104
\]

Next, we solve for \( x \):

\[
x = \frac{104}{13} = 8
\]

Now that we have the value of \( x \), we can find the lengths of each side:

1. First side:
\[
3x = 3 \times 8 = 24 \, \text{feet}
\]

2. Second side:
\[
4x = 4 \times 8 = 32 \, \text{feet}
\]

3. Third side:
\[
6x = 6 \times 8 = 48 \, \text{feet}
\]

Thus, the lengths of the sides of the triangle are:

- First side: 24 feet
- Second side: 32 feet
- Third side: 48 feet

To confirm, we check the perimeter:

\[
24 + 32 + 48 = 104 \, \text{feet}
\]

Everything checks out, so the measures of the sides of the triangle are:

\[
\boxed{24 \, \text{feet}, 32 \, \text{feet}, 48 \, \text{feet}}
\]