Question

The area of a rectangular flower bed is 24 square feet. The perimeter of the same flower bed is 22 feet. What are the dimensions of the flower bed? A. 2 ft by 12 ft B. 3 ft by 8 ft C. 3 ft by 6 ft D. 4 ft by 6 ft

Answer 1

The correct answer is option B. 3 ft by 8 ft

Explanation:

Points to remember

Area of rectangle = length * breadth

Perimeter of rectangle = 2(Length + Breadth)

It is given that, The area of a rectangular flower bed is 24 square feet. The perimeter of the same flower bed is 22 feet

To find the correct option

1). Check option A

Area = 2 * 12 = 24

Perimeter = 2( 2 + 12 ) = 28

False

2) Check option B

Area = 3 * 8 = 24

Perimeter = 2(3 + 8 ) = 22

True

3). Check option C

Area = 3 * 6 = 18

Perimeter = 2( 3 + 6 ) = 18

False

4). Check option D

Area = 4 * 6 = 24

Perimeter = 2( 4 +6 ) = 20

False

The correct answer is option B. 3 ft by 8 ft

Answer 2

B. 3 ft by 8 ft

EXPLANATION

The area is given as 24 square feet.

This implies that,

`l * w = 24`

The perimeter of the rectangular field is given as 22 feet.

This implies that,

`2(l + w) = 22`

Or

`l + w = 11`

We make w the subject in this last equation and put it inside the first equation.

`w = 11 - l`

When we substitute into the first equation we get;

`l(11 - l) = 24`

`11l - {l}^(2) = 24`

This implies that,

`{l}^(2) - 11l + 24 = 0`

`(l - 3)(l - 8) = 24`

`l = 3 \: or \: 8`

When l=3, w=24

Therefore the dimension is 3 ft by 8 ft