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34. If the perimeter of a rectangular house is

25 \frac{1}{3}

yards, and the l...

Nov 27, 2023

34. If the perimeter of a rectangular house is

25 \frac{1}{3}

yards, and the length is 22 feet. What is the width? 1. 16 feet 2. 35 feet 3. 37 feet 4. 40 feet 5. 42 feet

Key Concept

Perimeter of a rectangle and unit conversion

Explanation

The perimeter of a rectangle is given by the formula

P = 2l + 2w

, where

P

is the perimeter,

l

is the length, and

w

is the width. First, we need to convert the length from feet to yards by using the conversion factor

1 \text{ yard} = 3 \text{ feet}

. So,

22 \text{ feet} = \frac{22}{3} \text{ yards}

. The perimeter in yards is

25 \frac{1}{3} \text{ yards} = \frac{76}{3} \text{ yards}

. Plugging the length into the perimeter formula, we get

\frac{76}{3} = 2 \cdot \frac{22}{3} + 2w

. Solving for

w

, we find that

w = \frac{76}{3} - \frac{44}{3} = \frac{32}{3} \text{ yards}

, which is equivalent to

32 \text{ feet}

, but since this option is not available, we convert it back to yards to get

w = \frac{32}{3} \text{ yards} = 10 \frac{2}{3} \text{ yards}

. Since

10 \frac{2}{3} \text{ yards}

is not one of the options, we must have made a mistake in our conversion or calculation. Let's recheck the calculation:

\frac{76}{3} = 2 \cdot \frac{22}{3} + 2w

simplifies to

w = \frac{76 - 44}{6} = \frac{32}{6} = \frac{16}{3} \text{ yards}

, which is equivalent to

16 \text{ feet}

. Therefore, the correct answer is 16 feet.