Question

dracula takes a sheet of paper and cuts from one corner to the opposite corner, making two triangles. if the length of the cut is 40 inches and the paper is 22 inches wide, what is the length of the sheet of paper? provide an answer accurate to the nearest tenth.

Explanation:

Step1: Identify the triangle type

The paper is a rectangle, so cutting from corner to corner forms a right triangle. The cut is the hypotenuse (\(c = 40\) in), the width is one leg (\(a = 22\) in), and the length is the other leg (\(b\)) we need to find. Use the Pythagorean theorem: \(a^2 + b^2 = c^2\).

Step2: Rearrange the formula to solve for \(b\)

\(b^2 = c^2 - a^2\)

Step3: Substitute the known values

\(c = 40\), \(a = 22\), so \(b^2 = 40^2 - 22^2\)
\(40^2 = 1600\), \(22^2 = 484\), so \(b^2 = 1600 - 484 = 1116\)

Step4: Take the square root of \(b^2\)

\(b = \sqrt{1116}\)
Calculate \(\sqrt{1116} \approx 33.4\) (rounded to the nearest tenth)

Answer:

The length of the sheet of paper is approximately 33.4 inches.