Question

The length of a rectangle is 6 feet longer than three times it’s width if the area of the rectangle is 144 ft.² what is the width of the rectangle

Answer 1

Given:-

The length of a rectangle is 6 feet longer than three times its width.

Area of the rectangle is 144.

To find:-

The width and the length.

Assume that L is length and w is width.

So from the given data we have,

`l=6+3w`

gi1ven area is 144.

So the formula for area is,

`A=l* w`

Subsituting the known values we get,

`144=(6+3w)* w`

Simplifying the above equation we get,

`\begin{gathered} 3w^2+6w=144 \\ 3w^2+6w-144=0 \\ w^2+2w-48=0 \\ w^2+8w-6w-48=0 \end{gathered}`

So by simplifying furthur we get,

`\begin{gathered} w(w+8)-6(w+8)=0 \\ (w+8)(w-6)=0 \\ (w+8)=0,(w-6)=0 \\ w=-8,w=6 \end{gathered}`

The value of w is 6. ( we neglate -8 since width cannot be in negative )

Now we substitute the value of w in the equation L. we get,

`\begin{gathered} l=6+3w \\ l=6+3*6 \\ l=6+18 \\ l=24 \end{gathered}`

So the required value of length is 24ft and width is 6ft.