Question

1) You are designing a new kiddie soccer arena. The area of the rectangular

field needs to be 60 ft'. The length is 7 ft longer than the width. Find the
necessary dimensions.

Answer 1

The length of the rectangular field is 12 ft and the width is 5 ft.

Explanation:

The area of a rectangle is:

`\text{Area} = \text{length}* \text{width}`

The area of a rectangular field is, A = 60 ft.

The length of the field is:

l = w + 7

Compute the width of the field as follows:

`\text{Area} = \text{length}* \text{width}`

`60=(w+7)* w\\\\60=w^(2)+7w\\\\w^(2)+7w-60=0\\`

Factorize the last equation by splitting the middle term as follows:

`w^(2)+7w-60=0\\w^(2)+12w-5w-60=0\\w(w+12)-5(w+12)=0\\(w-5)(w+12)=0`

Now, since the width of rectangular field cannot be negative, the width is 5 ft.

Compute the length as follows:

l = w + 7

= 5 + 7

= 12

The length of the rectangular field is 12 ft.