the width of a rectangular field is 20 feet less than its length. the area of the field is 12,000 ft². what…

Explanation:

Step1: Define variables

Let the length of the field be (x) feet. Then the width is ((x - 20)) feet.

Step2: Use the area formula

The area of a rectangle is (A=\text{length}\times\text{width}). So, (x(x - 20)=12000). Expand the left - hand side: (x^{2}-20x=12000). Rearrange to get a quadratic equation: (x^{2}-20x - 12000=0).

Step3: Solve the quadratic equation

We can solve (x^{2}-20x - 12000=0) using the quadratic formula (x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}), where (a = 1), (b=-20), and (c=-12000). First, calculate the discriminant (\Delta=b^{2}-4ac=(-20)^{2}-4\times1\times(-12000)=400 + 48000=48400). Then (x=\frac{20\pm\sqrt{48400}}{2}=\frac{20\pm220}{2}). We have two solutions: (x_1=\frac{20 + 220}{2}=\frac{240}{2}=120) and (x_2=\frac{20-220}{2}=\frac{-200}{2}=-100). Since length cannot be negative, we discard (x_2=-100).

Answer:

C. (120) ft