Determine the missing length in the figure.
Understand the Problem
The question is asking to determine the missing length of a rectangle, given the area and one of the side lengths. This involves utilizing the formula for the area of a rectangle to find the unknown dimension.
Answer
The missing length is $4$ yards.
Answer for screen readers
The missing length of the rectangle is 4 yards.
Steps to Solve
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Identify the known values The area of the rectangle is given as $4 \frac{4}{5}$ square yards, and one of the lengths is $1 \frac{1}{5}$ yards.
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Convert mixed numbers to improper fractions Convert the given values to improper fractions for easier calculations.
- Area: $$ 4 \frac{4}{5} = \frac{24}{5} $$
- Length: $$ 1 \frac{1}{5} = \frac{6}{5} $$
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Use the area formula for rectangles The formula for the area $A$ of a rectangle is: $$ A = \text{length} \times \text{width} $$ In this case, we can rearrange the formula to find the missing length (width): $$ \text{width} = \frac{A}{\text{length}} $$
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Substitute known values into the formula Now substitute the known area and length into the equation: $$ \text{width} = \frac{\frac{24}{5}}{\frac{6}{5}} $$
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Perform the division of fractions To divide fractions, multiply by the reciprocal: $$ \text{width} = \frac{24}{5} \times \frac{5}{6} = \frac{24 \times 5}{5 \times 6} = \frac{24}{6} = 4 \text{ yards} $$
The missing length of the rectangle is 4 yards.
More Information
The calculation reveals that when dealing with areas, knowing one dimension allows you to easily find the other using the area formula. This approach is essential in geometry and can be applied to various real-world scenarios when dealing with rectangles.
Tips
- Not converting mixed numbers: Failing to convert mixed numbers into improper fractions can complicate the calculations. Always convert to improper fractions before proceeding.
- Incorrectly dividing fractions: Remember to multiply by the reciprocal when dividing fractions. This is a common mistake that can lead to errors in the final answer.
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