Question

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Explanation:

Step1: Recall area formula for rectangle

The area \( A \) of a rectangle is given by \( A = \text{length} \times \text{width} \), so to find the length \( l \), we can rearrange the formula to \( l=\frac{A}{\text{width}} \).

Step2: Convert mixed number to improper fraction

The width is \( 1\frac{1}{4}\text{ cm} \). Converting the mixed number to an improper fraction: \( 1\frac{1}{4}=\frac{1\times4 + 1}{4}=\frac{5}{4}\text{ cm} \).

Step3: Substitute values into the formula

We know the area \( A = 7\text{ cm}^2 \) and width \( w=\frac{5}{4}\text{ cm} \). Using \( l=\frac{A}{w} \), we substitute the values: \( l = \frac{7}{\frac{5}{4}} \).

Step4: Divide by a fraction (multiply by reciprocal)

Dividing by a fraction is the same as multiplying by its reciprocal, so \( \frac{7}{\frac{5}{4}}=7\times\frac{4}{5}=\frac{28}{5} = 5\frac{3}{5}\text{ cm} \).

Answer:

\( 5\frac{3}{5} \) (or \( \frac{28}{5} \))