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:
[tex]\text{Area} = \text{length}\times \text{width}[/tex]
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:
[tex]\text{Area} = \text{length}\times \text{width}[/tex]
[tex]60=(w+7)\times w\\\\60=w^{2}+7w\\\\w^{2}+7w-60=0\\[/tex]
Factorize the last equation by splitting the middle term as follows:
[tex]w^{2}+7w-60=0\\w^{2}+12w-5w-60=0\\w(w+12)-5(w+12)=0\\(w-5)(w+12)=0[/tex]
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.
