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:

$A=l\times w$

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

$P=22$

$2(l+w)=22$

$l+w=\dfrac{22}{2}$

$l=11-w$                       ...(i)

And,

$A=24$

$l\times w=24$              ...(ii)

Using (i) and (ii), we get

$(11-w)\times w=24$

$11w-w^2=24$

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

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

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.