ANSWER
B. 3 ft by 8 ft
EXPLANATION
The area is given as 24 square feet.
This implies that,
[tex]l \times w = 24[/tex]
The perimeter of the rectangular field is given as 22 feet.
This implies that,
[tex]2(l + w) = 22[/tex]
Or
[tex]l + w = 11[/tex]
We make w the subject in this last equation and put it inside the first equation.
[tex]w = 11 - l[/tex]
When we substitute into the first equation we get;
[tex]l(11 - l) = 24[/tex]
[tex]11l - {l}^{2} = 24[/tex]
This implies that,
[tex] {l}^{2} - 11l + 24 = 0[/tex]
[tex](l - 3)(l - 8) = 24[/tex]
[tex]l = 3 \: or \: 8[/tex]
When l=3, w=24
Therefore the dimension is 3 ft by 8 ft
Answer:
The correct answer is option B. 3 ft by 8 ft
Step-by-step 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
