Question

a rectangular yard measuring 30 ft by 49 ft is bordered (and surrounded) by a fence. inside, a walk that is 2 ft wide goes all the way along the fence. find the area of this walk. be sure to include the correct unit in your answer.

Explanation:

Step1: Calculate the area of the outer rectangle

The formula for the area of a rectangle is \(A = length\times width\). The outer rectangle has length \(l = 49\) ft and width \(w = 30\) ft. So, \(A_{outer}=49\times30 = 1470\) \(ft^{2}\).

Step2: Calculate the dimensions of the inner rectangle

Since the walk is 2 ft wide, the length of the inner rectangle \(l_{inner}=49 - 2\times2=49 - 4 = 45\) ft and the width of the inner rectangle \(w_{inner}=30 - 2\times2=30 - 4 = 26\) ft.

Step3: Calculate the area of the inner rectangle

Using the area formula \(A = length\times width\) again, \(A_{inner}=45\times26=1170\) \(ft^{2}\).

Step4: Calculate the area of the walk

The area of the walk \(A = A_{outer}-A_{inner}\). So, \(A = 1470-1170 = 300\) \(ft^{2}\).

Answer:

\(300\space ft^{2}\)