Question

the perimeter of a rectangle is 46 in and the length is 7 in more than the width. What are the dimensions of a rectangle

Answer 1

The perimeter of the rectangle is

`P=46in`

Let the length of the rectangle be

`=x`

Let the width of the rectangle be

`=y`

The length is 7 in more than the width, can be represented using the equation below

`x=(y+7)in\ldots\ldots\text{.}\mathrm{}(1)`

The perimeter of a rectangle is calculated using the formula below

`\begin{gathered} P=2(Length+breadth) \\ P=2(x+y)\ldots\text{.}(2) \end{gathered}`

Substitute the values of P=46 and equation (1) in equation (2)

`\begin{gathered} P=2(x+y) \\ 46=2(y+7+y) \\ 46=2(y+y+7) \\ 46=2(2y+7) \\ by\text{ expanding the bracket, we will have} \\ 46=4y+14 \\ 4y+14=46 \end{gathered}`

Subtract 14 from both sides

`\begin{gathered} 4y+14=46 \\ 4y+14-14=46-14 \\ 4y=32 \end{gathered}`

Divide both sides by 4

`\begin{gathered} 4y=32 \\ (4y)/(4)=(32)/(4) \\ y=8 \end{gathered}`

Substitute the value of y= 8 in equation (1)

`\begin{gathered} x=y+7 \\ x=8+7 \\ x=15 \end{gathered}`

Therefore,

The length of the rectangle = 15 in

The