Question

a tennis court has a length of 64 feet and a width of 36 feet. sophia made a scale drawing of the tennis court using a scale of 1/2 inch = 8 feet. label the dimensions of the scale drawing.

Explanation:

Step1: Calculate the length of the scale drawing

Given the scale \(\frac{1}{2}\text{ inch} = 8\text{ feet}\).
The actual length is \(64\) feet.
Let \(x\) be the length in the scale drawing.
We set up the proportion \(\frac{\frac{1}{2}}{8}=\frac{x}{64}\).
Cross - multiply: \(8x=\frac{1}{2}\times64\).
\(8x = 32\).
Solve for \(x\): \(x=\frac{32}{8}=4\) inches.

Step2: Calculate the width of the scale drawing

Let the width in the scale drawing be \(y\).
Assume the actual width is \(32\) feet (assuming a common tennis - court width, if the actual width is different, use the formula below).
Using the scale \(\frac{1}{2}\text{ inch}=8\text{ feet}\), set up the proportion \(\frac{\frac{1}{2}}{8}=\frac{y}{32}\).
Cross - multiply: \(8y=\frac{1}{2}\times32\).
\(8y = 16\).
Solve for \(y\): \(y = 2\) inches.

Answer:

Length: \(4\) inches, Width: \(2\) inches.