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?

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:

$\text {area of rectangle }=\text { length } \times \text { width }$

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)

$(x-80)(x-60)=\text { length } \times(x-60)\\\\length = \frac{(x-80)(x-60)}{(x-60)}$

Cancelling (x - 60)

length = (x - 80)

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