Question

gwen takes a rectangular piece of fabric and makes a diagonal cut from one corner to the opposite corner. the cut she makes is 5.7 inches long and the width of the fabric is 4.7 inches. what is the fabrics length? if necessary, round to the nearest tenth.

inches

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Explanation:

Step1: Recall the Pythagorean theorem

For a rectangle, the diagonal \( d \), length \( l \), and width \( w \) satisfy \( d^{2}=l^{2}+w^{2} \). We need to solve for \( l \), so we can rearrange the formula to \( l = \sqrt{d^{2}-w^{2}} \).

Step2: Substitute the given values

We know that \( d = 5.7 \) inches and \( w = 4.7 \) inches. First, calculate \( d^{2}-w^{2} \):
\( d^{2}-w^{2}=(5.7)^{2}-(4.7)^{2} \)
\( = 32.49 - 22.09 \)
\( = 10.4 \)

Step3: Calculate the length

Now, take the square root of \( 10.4 \) to find \( l \):
\( l=\sqrt{10.4}\approx3.2 \) (rounded to the nearest tenth)

Answer:

\( 3.2 \)