Question

Carlos is putting a rectangular swimming pool in his back yard. The length of the pool is `12` feet `6` inches. The width is `30` feet `4` inches. He wants to put in a sidewalk around the pool that is `2` feet wide.What is the length in feet only? In other words, convert `12` feet `6` inches to a decimal number, rounded to the nearest hundredth.What is the width in feet only? In other words, convert 30 feet 4 inches to a decimal number, rounded to the nearest hundredth.Use the feet dimensions to find the total area of the sidewalk. Round to the nearest hundredth.

Answer 1

Remember that 1 foot is equal to 12 inches.

a)

To find the length in feet only, convert 6 inches to feet and add that amount to the length of 12 feet:

$\begin{gathered} 6in=6in\times\frac{1ft}{12in}=0.5ft \\ \\ 12ft+6in=12ft+0.5ft=12.5ft \end{gathered}$

Then, the length of the swimming pool in feet is 12.50.

b)

To find the width in feet only, convert 4 inches to feet and and that amount to the width of 30 feet:

$\begin{gathered} 4in=4in\times\frac{1ft}{12in}=0.333...ft\approx0.33ft \\ \\ 30ft+4in=30ft+0.33ft=30.33ft \end{gathered}$

Then, the wudth of the swimming pool in feet (to the nearest hundredth) is 30.33.

c)

Draw a diagram of the pool with the sidewalk to visualize the situation:

The width and the length of the larger rectangle that includes the sidewalk are 4ft larger than the dimensions of the swimming pool because the sidewalk is 2ft wide.

To find the area of the sidewalk, subtract the area of the smaller rectangle from the area of the larger rectangle:

$\begin{gathered} A_{large}=(34.33ft)\times(16.50ft)=566.445ft^2 \\ A_{small}=(30.33ft)\times(12.50)=379.125ft^2 \\ \\ A_{sidewalk}=A_{large}-A_{small} \\ =566.445ft^2-379.125ft^2 \\ =187.32ft^2 \end{gathered}$

Then, the area of the sidewalk is 187.32 square feet.