Question

The width of a rectangular field is 20 feet less than its length. The area of the field is 12,000 ft2. What is the length of the field?

80 ft
100 ft
120 ft
140 ft

Answer 1

120 ft

Explanation:

Let's assume that the length of the field is x feet. Then, according to the problem statement, the width of the field is (x - 20) feet.

The area of a rectangle is given by the formula A = length x width. So, we can write:

x(x - 20) = 12,000

Expanding the left-hand side, we get:

x^2 - 20x = 12,000

Bringing all the terms to one side, we have:

x^2 - 20x - 12,000 = 0

Now, we can solve this quadratic equation using the quadratic formula:

x = (-(-20) ± sqrt((-20)^2 - 4(1)(-12,000))) / (2(1))

x = (20 ± sqrt(20^2 + 48,000)) / 2

x = (20 ± 220) / 2

We discard the negative root, since a length cannot be negative, and we get:

x = 120

Therefore, the length of the field is 120 feet.