Question

margarita is installing a new patio. she uses pavers that are made from recycled materials. she drew a sketch to show how her patio is going to look so she knows what materials to buy at the store. the dimensions of the rectangular patio in her sketch are: the width is 4 centimeters. the length is 7 centimeters. enter the scale. 2 cm : 25 ft. enter the actual width, w, of the patio. feet enter the actual length, p, of the patio. feet i want to do this optional task to determine the actual width, w. write a proportion using the variable w. then solve for w using means and extremes. i want to do this optional task to determine the actual length, p. write a proportion using the variable p. then solve for p using means and extremes. the area of the patio is square feet.

Explanation:

Step1: Set up proportion for width

The scale is 2 cm : 25 ft. The width on the sketch is 4 cm. Let the actual width be $w$. The proportion is $\frac{2}{25}=\frac{4}{w}$.

Step2: Solve proportion for width

Cross - multiply: $2w = 4\times25$. So, $2w=100$. Then, divide both sides by 2: $w = 50$ ft.

Step3: Set up proportion for length

The length on the sketch is 7 cm. Let the actual length be $p$. The proportion is $\frac{2}{25}=\frac{7}{p}$.

Step4: Solve proportion for length

Cross - multiply: $2p=7\times25$. So, $2p = 175$. Then, divide both sides by 2: $p = 87.5$ ft.

Step5: Calculate area of the patio

The area of a rectangle is $A = p\times w$. Substitute $p = 87.5$ ft and $w = 50$ ft. So, $A=87.5\times50 = 4375$ square feet.

Answer:

The actual width of the patio is 50 ft, the actual length of the patio is 87.5 ft, and the area of the patio is 4375 square feet.