Question

1. a rancher uses 280 feet of fencing to build a rectangular corral for a horse. the length of the corral is 2.5 times the width. what is the area of the corral? a 112 square feet c 4,000 square feet b 700 square feet d 16,000 square feet

Explanation:

Step1: Let the width be \(x\)

Let the width of the rectangular corral be \(x\) feet. Since the length is \(2.5\) times the width, the length is \(2.5x\) feet.

Step2: Use the perimeter formula

The perimeter formula of a rectangle is \(P = 2(l + w)\). Given \(P=280\) feet, \(l = 2.5x\), and \(w=x\).
Substitute into the formula: \(280=2(2.5x + x)\)
Simplify the right - hand side: \(280=2\times3.5x\), so \(280 = 7x\)
Solve for \(x\): \(x=\frac{280}{7}=40\)

Step3: Find the length

Since \(l = 2.5x\) and \(x = 40\), then \(l=2.5\times40 = 100\)

Step4: Calculate the area

The area formula of a rectangle is \(A=l\times w\). Substitute \(l = 100\) and \(w = 40\)
\(A=100\times40=4000\)

Answer:

C. 4,000 square feet