Question

Mitch takes a rectangular piece of fabric and cuts from one corner to the opposite corner. If the piece of fabric is 6.9 inches long and 4.8 inches wide, how long is the diagonal cut that Mitch made? If necessary, round to the nearest tenth.

Answer 1

To find the length of the diagonal cut that Mitch made, we can use the Pythagorean theorem. The diagonal \(d\) of a rectangle can be found using the formula:

\[
d = \sqrt{l^2 + w^2}
\]

where \(l\) is the length and \(w\) is the width of the rectangle. Here, \(l = 6.9\) inches and \(w = 4.8\) inches.

Now, we can calculate:

1. Square the length and width:

\[
l^2 = (6.9)^2 = 47.61
\]

\[
w^2 = (4.8)^2 = 23.04
\]

2. Add these squares together:

\[
l^2 + w^2 = 47.61 + 23.04 = 70.65
\]

3. Take the square root of the sum:

\[
d = \sqrt{70.65} \approx 8.4 \, \text{inches}
\]

Thus, the length of the diagonal cut that Mitch made is approximately **8.4 inches** when rounded to the nearest tenth.