Question

sandra takes a sheet of paper and makes a diagonal cut from one corner to the opposite corner, making two triangles. the cut she makes is 26 centimeters long and the width of the paper is 24 centimeters. what is the papers length?

□ centimeters

Explanation:

Step1: Identify the problem type

This is a right triangle problem where the diagonal of the rectangle (paper) is the hypotenuse, and the width and length are the legs. We can use the Pythagorean theorem, \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse (diagonal), and \(a\) and \(b\) are the legs (width and length). Let the length be \(l\), width \(w = 24\) cm, and diagonal \(d = 26\) cm. So we have \(w^2 + l^2 = d^2\).

Step2: Rearrange the formula to solve for length

We can rearrange the Pythagorean theorem to solve for \(l\): \(l^2 = d^2 - w^2\).

Step3: Substitute the known values

Substitute \(d = 26\) and \(w = 24\) into the formula: \(l^2 = 26^2 - 24^2\). Calculate \(26^2 = 676\) and \(24^2 = 576\). Then \(l^2 = 676 - 576 = 100\).

Step4: Solve for \(l\)

Take the square root of both sides: \(l=\sqrt{100} = 10\).

Answer:

10