Question

A rectangular countertop has a perimeter of 22 feet and an area of 24 square feet what are the dimensions of the counter

Answer 1

Given:

A rectangular counter-top has a perimeter of 22 feet and an area of 24 square feet.

To find:

The dimensions of the counter.

Solution:

Let l is the length and w is the width of a rectangle, then

Perimeter of a rectangle is:

`P=2(l+w)`

Area of the rectangle is:

`A=l* w`

A rectangular counter-top has a perimeter of 22 feet and an area of 24 square feet.

`P=22`

`2(l+w)=22`

`l+w=(22)/(2)`

`l=11-w` ...(i)

And,

`A=24`

`l* w=24` ...(ii)

Using (i) and (ii), we get

`(11-w)* w=24`

`11w-w^2=24`

`0=24-11w+w^2`

`w^2-11w+24=0`

Splitting the middle term, we get

`w^2-8w-3w+24=0`

`w(w-8)-3(w-8)=0`

`(w-8)(w-3)=0`

`w=8,3`

For
`w=8`,

`l=11-8`

`l=3`

For
`w=3`,

`l=11-3`

`l=8`

Therefore, the dimensions of the rectangular counter top are 3 feet by 8 feet.