Question

Molly wants her rectangular rooftop garden plot to have an area of 21 square feet. If she makes the width 5 feet, what must be the length? is this an example of direct variation or inverse variation?

A)105 ft; direct
B)4.2 ft;direct
C)4.2 ft; inverse
D)105 ft;inverse

Answer 1

Option C.

Explanation:

Molly wants her rectangular rooftop garden to have the area = 21 feet²

Width of the rectangular garden is = 5 feet

Let the length of the garden = l feet

Since we know the formula of "area of the garden = Length × width"

Length =
`\frac{\text{Area of the garden}}{\text{Width}}`

This formula represents length of the garden ∝
`\frac{1}{\text{Width}}`

Length of the garden is inversely proportional to the width of the garden.

(Length increases with the decrease in width)

Now we plug in the values in the formula.

l =
`(21)/(5)`

= 4.2 feet

Option C. is the answer.

Answer 2

Area = length x width
21 = length x 5
length = 21/5 = 4.2

The length is inversely proportional to the width because as the length increases the width reduces and vice-versa