Chapter 6, Problem 3PFA

a.

To determine

To find: The dimensions of vegetable garden of given parameter.

Answer to Problem 3PFA

The option D is correct.

Explanation of Solution

Given:

The perimeter of the vegetable garden is 48 feet the length is 6 feet more than width shown in Figure-1 here.

Formula/ concept used:

The perimeter of rectangle is P = 2(length + width)

Calculations:

The length and width of the garden are x ft. and ( x -6) ft. respectively.

Therefore, the perimeter of the garden is P = 2 ( x + x -6) = 4x -12 feet. But the perimeter of the garden is 48 feet.

  $\Rightarrow 4x-12=48$

  $\Rightarrow 4x=48+12=60$

  $\Rightarrow x=\frac{60}{4}=15$ ft.

Thus, the length of the garden is 15 feet and the width (15 − 6) = 9 ft.

Conclusion:

The option D is correct.

b.

To determine

To find: The area of vegetable garden described in part (a)

Answer to Problem 3PFA

The area of the vegetable garden is $135$ sq. ft.

Explanation of Solution

Given:

The length of the vegetable garden is 15 feet and the width 9 feet.

Concept used:

The area of a rectangle is A = length × width.

Calculations:

The length of the garden is 15 feet and width 9 feet.

Therefore, the area of the vegetable garden is $A=15\times 9=135$ sq. ft.

Conclusion:

The area of the vegetable garden is $135$ sq. ft.