A farmer has a large field that is x feet in length. He wants to fence in a rectangular section in the middle of the field, leaving a length of 100 feet of open field beyond each end of the fenced rectangle. He also wants the width of the fenced-in space to be 100 feet less than its length, as shown in the diagram.

Find the equation in standard form for the area of the fenced-in section in terms of the length of the field.

(area = length • width)

Question

Mathematics

Belch

9 February, 02:12

A farmer has a large field that is x feet in length. He wants to fence in a rectangular section in the middle of the field, leaving a length of 100 feet of open field beyond each end of the fenced rectangle. He also wants the width of the fenced-in space to be 100 feet less than its length, as shown in the diagram.

Find the equation in standard form for the area of the fenced-in section in terms of the length of the field.

(area = length • width)

+1

Answers (1)

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Anabelle · Answer 1

y = x2 - 500x + 60,000

Step-by-step explanation:

The length of the fenced-in section is (x - 200) feet, and the width is (x - 300) feet.

area of the fenced-in section = length • width

y = (x - 200) (x - 300)

= x2 - 300x - 200x + 60,000

= x2 - 500x + 60,000