Question

Tessa takes a rectangular piece if fabric and makes a diagonal cut from one corner to the opposite corner. The cut she makes is 5 inches long and the width of the fabric is 3 inches. The fabric's length is __ inches.

Answer 1

Consider the following schematic diagram,

Note that the diagonal cut will divide the rectangle into two congruent right triangles.

The right triangle has the hypotenuse 5 inches and width 3 inches, so the length can be calculated using Pythagoras theorem as follows,

$\begin{gathered} \text{ Hypotenuse}^2=\text{Length}^2+\text{Width}^2 \\ 5^2=\text{Length}^2+\text{3}^2 \\ \text{Length}^2=5^2-3^2 \\ \text{Length}^2=25-9 \\ \text{Length}^2=16 \\ \text{Length}=\sqrt[]{16} \\ \text{Length}=4 \end{gathered}$

Thus, the fabric's length is 5 inches.