Question

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

Answer 1

Answer:

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

Step-by-step explanation:

The area of a rectangle is:

$\text{Area} = \text{length}\times \text{width}$

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:

$\text{Area} = \text{length}\times \text{width}$

$60=(w+7)\times w\\\\60=w^{2}+7w\\\\w^{2}+7w-60=0$

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.