Question

A rectangles length is $7$ inches lager than its width.

If the perimeter of the rectangle is $110$ inches, find its length and width.

Answer 1

Find the length and width of the rectangle:

Perimeter of rectangle is $110$

Length of rectangle is $L$

Width of rectangle is $W$

Expression for the Perimeter can be expressed as,

$P=2\left(L+W\right)$

Substitute $P=110$in the above equation

$110=2L+2W......\left(1\right)$

if the length is $7$ inches more than the width, then that can be expressed as,

$L=7+W......\left(2\right)$

Step-1: Find the width of of the rectangle:

Now we will substitute $7+W$ for $L$in equation $\left(1\right)$ becomes,

$$\begin{gathered} \Rightarrow 110=2\left(7+W\right)+2W \\ \Rightarrow 110=14+2W+2W \\ \Rightarrow 110=14+4W \\ \Rightarrow 110-14=4W \\ \Rightarrow 96=4W \\ \Rightarrow \frac{96}{4}=W \\ \Rightarrow W=24 \end{gathered}$$

Step-2: Find the length of of the rectangle

Substitute $W=24$ in the Equation $\left(2\right)$ becomes,

$$\begin{gathered} L=7+W \\ L=7+24 \\ L=31 \end{gathered}$$

Hence, the Length of the rectangle is $31$ and the width of the rectangle is $24$.