Question

a rectangular swimming pool with length ( b ) and width ( h ) is surrounded by a walkway that is 3 feet wide. which equation below could be used to find the area of the walkway?
( a=(b + 6)(h + 6)-bh )
( a=bh-(b + 6)(h + 6) )
( a=(b + 3)(h + 3)-bh )
( a=(b + 6)(h + 6) )

Explanation:

Step1: Analyze the dimensions of the outer rectangle

Since the walkway is 3 feet wide on both sides of the pool (length and width), the length of the outer rectangle is \(b + 3+3=b + 6\) and the width of the outer rectangle is \(h+3 + 3=h + 6\). The area of the outer rectangle (pool + walkway) is \(A_{outer}=(b + 6)(h + 6)\) using the formula for the area of a rectangle \(A = lw\) (where \(l\) is length and \(w\) is width).

Step2: Analyze the area of the pool

The area of the pool is \(A_{pool}=bh\) using the formula for the area of a rectangle \(A = lw\) (where \(l = b\) and \(w = h\)).

Step3: Calculate the area of the walkway

The area of the walkway \(A\) is the area of the outer rectangle (pool + walkway) minus the area of the pool. So, \(A=(b + 6)(h + 6)-bh\).

Answer:

\(A=(b + 6)(h + 6)-bh\) (the fourth option)