Question

hercules takes a sheet of paper and cuts from one corner to the opposite corner, making two triangles. if the length of the cut is 34 inches and the paper is 7 inches wide, what is the length of the sheet of paper? provide an answer accurate to the nearest tenth. 34 in 7 in length label required skill code 79011

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs of the right - triangle. Let the width of the paper \(a = 7\) inches, the length of the paper \(b\), and the length of the cut (hypotenuse) \(c = 34\) inches. Then the formula becomes \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute the values

Substitute \(a = 7\) and \(c = 34\) into the formula \(b^{2}=c^{2}-a^{2}\). So \(b^{2}=34^{2}-7^{2}\).
First, calculate \(34^{2}=34\times34 = 1156\) and \(7^{2}=7\times7 = 49\). Then \(b^{2}=1156 - 49=1107\).

Step3: Solve for \(b\)

Take the square root of both sides. \(b=\sqrt{1107}\approx33.3\)

Answer:

\(33.3\) inches