Question

You are cutting a rectangular piece of fabric in half along a diagonal. The fabric measures $28inches$ wide and $1\frac{1}{4}yards$ long. What is the length (in inches) of the diagonal?

Answer 1

Find the length of the diagonal of a rectangular piece of fabric.

We have given that, the length of a rectangular piece of fabric, $l=1\frac{1}{4}yd$

$=\frac{5}{4}yd$

$$\begin{gathered} =\frac{5}{4}\times 36in. \\ =45in. \end{gathered}$$

Width of a rectangular piece of fabric, $b=28inches$

We know the length of a diagonal of a rectangle $=\sqrt{l^2+b^2}$, where$l$ is the length and $b$ is the breadth of the rectangle.

By Substituting the values of $l$ and $b$ in the formula we get,

The length of a diagonal of a given rectangle $=\sqrt{{45}^2+{28}^2}$

$$\begin{gathered} =\sqrt{2025+784} \\ =\sqrt{2809} \\ =53in. \end{gathered}$$

Hence, the length of a diagonal of a rectangle is $53in.$