Question

the dimensions of the regulation basketball court are: the length is 24 feet. the width is 50 feet. enter the scale. blueprint: 3 in. 20 ft. = 3 in. : 20 ft. actual court: 24 ft. 50 ft. enter the length, in of the blueprint. 12.6 inches enter the width, in of the blueprint. 7.5 inches the area of the blueprint is square inches.

Explanation:

Step1: Understand the scale

The scale is \( 3 \text{ in.} : 20 \text{ ft} \), which means 3 inches on the blueprint represent 20 feet in actual.

Step2: Find the length on blueprint

Actual length is 24 feet. Let \( x \) be the length on blueprint. Set up proportion:
\( \frac{3}{20} = \frac{x}{24} \)
Cross - multiply: \( 20x = 3\times24 \)
\( 20x = 72 \)
\( x=\frac{72}{20}=3.6 \) inches

Step3: Find the width on blueprint

Actual width is 50 feet. Let \( y \) be the width on blueprint. Set up proportion:
\( \frac{3}{20}=\frac{y}{50} \)
Cross - multiply: \( 20y = 3\times50 \)
\( 20y = 150 \)
\( y = \frac{150}{20}=7.5 \) inches

Step4: Find the area of actual court

Area of a rectangle is \( \text{length}\times\text{width} \). So actual area is \( 24\times50 = 1200 \) square feet.

Step5: Find the area of blueprint court

First, convert blueprint length and width to the same unit (inches, but we can also use the scale factor for area). The scale factor for length (and width) is \( \frac{3}{20\times12}=\frac{3}{240}=\frac{1}{80} \) (since 20 feet = 240 inches). The area scale factor is \( (\frac{1}{80})^2=\frac{1}{6400} \). But we can also calculate using the blueprint dimensions. Blueprint length is 3.6 inches, blueprint width is 7.5 inches. Area of blueprint is \( 3.6\times7.5 = 27 \) square inches.

Answer:

• Blueprint length: \( 3.6 \) inches
• Blueprint width: \( 7.5 \) inches
• Actual area: \( 1200 \) square feet
• Blueprint area: \( 27 \) square inches