Question

The length of a rectangle is twice the width. If the perimeter is 282, find both dimensions.

Answer 1

The value of the length and width is;

`\begin{gathered} \text{length }l=94\text{ units} \\ \text{width }w=47\text{ units} \end{gathered}`

Step-by-step explanation:

Let l and w represent the length and width of the rectangle.

Given that;

The length of a rectangle is twice the width

`l=2w\text{ ------1}`

the perimeter is 282.

the formula for perimeter of a rectangle is;

`\begin{gathered} P=2l+2w \\ \sin ce; \\ P=282 \\ 2l+2w=282\text{ -----------2} \end{gathered}`

Let us substitute equation 1 to 2;

`\begin{gathered} 2l+2w=282\text{ } \\ 2(2w)+2w=282\text{ } \\ 4w+2w=282 \\ 6w=282 \\ w=(282)/(6) \\ w=47\text{ units} \end{gathered}`

We can now substitute the value of w into equation 1 to get the length l;

`\begin{gathered} l=2w \\ l=2(47) \\ l=94\text{ units} \end{gathered}`

Therefore, the value of the length and width is;

`\begin{gathered} \text{length }l=94\text{ units} \\ \text{width }w=47\text{ units} \end{gathered}`