Question

irma takes a rectangular piece of fabric and cuts from one corner to the opposite corner. if the piece of fabric is 3 inches long and 6 inches wide, how long is the diagonal cut that irma made? if necessary, round to the nearest tenth. inches

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 3\) (length of the rectangle), \(b = 6\) (width of the rectangle), and \(c\) is the diagonal.
Substitute \(a = 3\) and \(b = 6\) into the formula: \(3^{2}+6^{2}=c^{2}\).
Calculate \(3^{2}=9\) and \(6^{2}=36\), so \(9 + 36=c^{2}\), which simplifies to \(c^{2}=45\).

Step2: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{45}\).
Simplify \(\sqrt{45}=\sqrt{9\times5}=3\sqrt{5}\approx 3\times2.236 = 6.708\).
Round \(6.708\) to the nearest tenth: \(6.7\).

Answer:

\(6.7\)