Question

a path around a rectangular field measures 300 meters in length. if the length of the field is 100 meters, what is the width of the field?
a. 100 meters
b. 50 meters
c. 25 meters
d. 15 meters

Explanation:

Step1: Recall the formula for the perimeter of a rectangle

The perimeter \(P\) of a rectangle is given by \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width. Here, \(P=300\) meters and \(l = 100\) meters.

Step2: Substitute the values into the formula

Substitute \(P = 300\) and \(l=100\) into \(P = 2(l + w)\). We get \(300=2(100 + w)\).
First, divide both sides of the equation by \(2\): \(\frac{300}{2}=\frac{2(100 + w)}{2}\), which simplifies to \(150=100 + w\).

Step3: Solve for \(w\)

Subtract \(100\) from both sides of the equation \(150=100 + w\). So, \(w=150 - 100\).

Answer:

B. 50 meters