Question

The perimeter of a rectangle is 46 inches. The length is 2 inches less than 4 times the width.Find the length and the width.

Answer 1

• Length=18 inches

,

• Width=5 inches

Step-by-step explanation:

• Let the width of the rectangle = w inches

,

•

The length is 2 inches less than 4 times the width.

• Length of the rectangle = (4w-2) inches

,

•

We are told that the perimeter of a rectangle = 46 inches.

The perimeter of a Rectangle=2(Length+Width)

Substituting the given values, we have:

`46=2(4w-2+w)`

We solve for w.

`\begin{gathered} 46=2(4w+w-2) \\ \text{Divide both sides by 2} \\ (46)/(2)=(2(4w+w-2))/(2) \\ 23=5w-2 \\ \text{Add 2 to both sides} \\ 23+2=5w-2+2 \\ 5w=25 \\ \text{Divide both sides by 2} \\ (5w)/(5)=(25)/(5) \\ w=5\text{ inches} \end{gathered}`

We then solve for the length.

`\begin{gathered} \text{Length}=4w-2 \\ =4(5)-2 \\ =20-2 \\ =18\text{ inches} \end{gathered}`

The length of the rectangle is 18 inches and the width is 5 inches.