Question

The width of a rectangle is six less than twice the length. The perimeter is $18$. Find the length and width.

Short answer

The length is$5$and width is$4$.

Step-by-step solution

Step 1. Given information

The width of a rectangle is six less than twice the length. The perimeter is $18$

Step 2. Finding unknown

Let the length of rectangle be x

Therefore the width is $b=2x-6$

According to question,

role="math" localid="1647145974094" $$\begin{gathered} 2(l+b)=18 \\ 2(x+2x-6)=18 \\ 2(3x-6)=18 \\ 6x-12=18 \\ 6x=30 \\ x=5=l \end{gathered}$$

And width is

$$\begin{gathered} b=2x-6 \\ =2\times 5-6 \\ =10-6 \\ =4 \end{gathered}$$