Question

a swimming pool has a 3 - foot wide cement walkway around its perimeter as shown.write an expression, in factored form, that represents the area (in square feet) of the cement walkway.ft²

Explanation:

Step1: Calculate the outer rectangle's dimensions

The width of the outer rectangle is \(12 + 3+3=18\) feet. The length of the outer rectangle is \((4x + 2)+3 + 3=4x+8\) feet.

Step2: Calculate the area of the outer rectangle

Using the formula \(A = lw\) (where \(l\) is length and \(w\) is width), the area of the outer rectangle \(A_{outer}=18(4x + 8)=72x+144\) square feet.

Step3: Calculate the area of the inner (pool) rectangle

The area of the inner rectangle \(A_{inner}=12(4x + 2)=48x+24\) square feet.

Step4: Calculate the area of the walk - way

The area of the walk - way \(A = A_{outer}-A_{inner}\).

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Answer:

\(24(x + 5)\)