14. A triangle has two equal sides. The third side has a length of 13 feet, 2 inches. If the perimeter of the triangle is 40 feet, what is the length of one of the equal sides?

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We start by letting the length of each of the equal sides be $$ x $$ feet. The triangle has one side that measures 13 feet 2 inches. First, we convert this length entirely into feet:

$$
13 \text{ feet } 2 \text{ inches } = 13 + \frac{2}{12} = 13 + \frac{1}{6} = \frac{79}{6} \text{ feet.}
$$

Since the perimeter of the triangle is 40 feet, we set up the equation:

$$
x + x + \frac{79}{6} = 40.
$$

Simplify and solve for $$ x $$:

$$
2x + \frac{79}{6} = 40.
$$

Subtract $$\frac{79}{6}$$ from both sides:

$$
2x = 40 - \frac{79}{6}.
$$

Express 40 as a fraction with denominator 6:

$$
40 = \frac{240}{6},
$$

so we have:

$$
2x = \frac{240}{6} - \frac{79}{6} = \frac{240 - 79}{6} = \frac{161}{6}.
$$

Divide both sides by 2:

$$
x = \frac{161}{6 \times 2} = \frac{161}{12}.
$$

Thus, one of the equal sides is

$$
\frac{161}{12} \text{ feet,}
$$

which can be written as a mixed number:

$$
\frac{161}{12} = 13\frac{5}{12} \text{ feet.}
$$
One of the equal sides is $$ 13 \frac{5}{12} $$ feet long.

14. A triangle has two equal sides. The third side has a length of 13 feet, 2 inches. If the perimeter of the triangle is 40 feet, what is the length of one of the equal sides?

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