Question

a rectangular garden measures 21 ft by 42 ft. surrounding (and bordering) the garden is a path 2 ft wide. find the area of this path. be sure to include the correct unit in your answer.

Explanation:

Step1: Calculate the outer rectangle's dimensions

The garden has length \( l = 42\) ft and width \( w = 21\) ft. The path is \( 2\) ft wide.
The outer - rectangle length \( L=42 + 2+2=46\) ft (adding \( 2\) ft on each side), and the outer - rectangle width \( W=21 + 2+2=25\) ft (adding \( 2\) ft on each side).

Step2: Calculate the areas of the outer and inner rectangles

The area of a rectangle is \( A = lw\).
The area of the outer rectangle \(A_{outer}=L\times W=46\times25 = 1150\) \(ft^{2}\).
The area of the inner rectangle (the garden) \(A_{inner}=l\times w=42\times21 = 882\) \(ft^{2}\).

Step3: Calculate the area of the path

The area of the path \(A = A_{outer}-A_{inner}\).
\(A=1150 - 882=268\) \(ft^{2}\).

Answer:

\(268\) \(ft^{2}\)