The perimeter of a triangle is $$ 27 \frac{2}{3} \mathrm{ft} $$. Two of the sides measure $$ 10 \frac{1}{6} \mathrm{f} $$. each. What is the length of the third side? Circle your final answer.

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First, convert all mixed numbers to improper fractions.

For the perimeter:
 27 2/3 ft = (27 × 3 + 2)⁄3 = 83⁄3 ft.

For each given side:
 10 1/6 ft = (10 × 6 + 1)⁄6 = 61⁄6 ft.

Since the triangle has two sides of length 61⁄6 ft each, the sum of these two is:
 2 × (61⁄6) = 122⁄6 = 61⁄3 ft.

Now, subtract this sum from the perimeter to find the third side:
 Third side = (83⁄3) − (61⁄3) = (83 − 61)⁄3 = 22⁄3 ft.

Convert 22⁄3 ft to a mixed number:
 22 ÷ 3 = 7 with a remainder of 1, so 22⁄3 = 7 1/3 ft.

Thus, the length of the third side is Ⓞ 7 1/3 ft.
The length of the third side is $$ 7 \frac{1}{3} $$ feet.

The perimeter of a triangle is \( 27 \frac{2}{3} \mathrm{ft} \). Two of the sides measure \( 10 \frac{1}{6} \mathrm{f} \). each. What is the length of the third side? Circle your final answer.

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