Question

The area in square feet of a rectangular field is x2 - 140x + 4800. The width, in feet, is x-60. What is the length, in feet?

The length, in feet, is

Answer 1

The length in feet is (x - 80) feet

Solution:

The area in square feet of a rectangular field is
`x^2 - 140x + 4800`

The width, in feet, is x - 60

To find: length in feet

The area of rectangle is given as:

`\text {area of rectangle }=\text { length } * \text { width }`

Now we can simplify area

area =
`x^2 - 140x + 4800`

-140x can be rewritten as -80x - 60x

`area = x^2 -80x -60x + 4800`

Taking "x" as common from first two terms and -60 as common from last two terms

area = x(x - 80) -60(x - 80)

Taking (x - 80) as common term

Area = (x - 80)(x - 60)

Substitute area = (x - 80)(x - 60) and width = (x - 60)

`(x-80)(x-60)=\text { length } *(x-60)\\\\length = ((x-80)(x-60))/((x-60))`

Cancelling (x - 60)

length = (x - 80)

Thus the length in feet is (x - 80) feet