Question

seiki is a city planner. she is planning to install a high - school regulation rectangular basketball court in a local park. she draws a blueprint that is the same shape as the court for the cement contractor. on the blueprint, 3 inches represents 20 feet on the court. the dimensions of the regulation basketball court are: the length is 84 feet. the width is 50 feet. enter the scale. blueprint: 3 in. : 20 ft court enter the length, b, of the blueprint. i want to do this optional task to determine the length, b. write a proportion using the variable b. then solve for b using means and extremes. blueprint: court enter the width, w, of the blueprint. i want to do this optional task to determine the width, w. write a proportion using the variable w. then solve for w using means and extremes. the area of the blueprint is square inches.

Explanation:

Step1: Set up proportion for length

The scale is 3 in. : 20 ft. Let the length of the blueprint be $b$ inches and the actual - length is 84 ft. The proportion is $\frac{3}{20}=\frac{b}{84}$.

Step2: Solve for $b$ using cross - multiplication

Cross - multiplying gives $20b = 3\times84$. So, $20b=252$. Then $b=\frac{252}{20}=12.6$ inches.

Step3: Set up proportion for width

Let the width of the blueprint be $w$ inches and the actual width is 50 ft. The proportion is $\frac{3}{20}=\frac{w}{50}$.

Step4: Solve for $w$ using cross - multiplication

Cross - multiplying gives $20w = 3\times50$. So, $20w = 150$. Then $w=\frac{150}{20}=7.5$ inches.

Step5: Calculate the area of the blueprint

The area of a rectangle is $A = b\times w$. Substituting $b = 12.6$ inches and $w = 7.5$ inches, we get $A=12.6\times7.5 = 94.5$ square inches.

Answer:

The length of the blueprint, $b = 12.6$ inches.
The width of the blueprint, $w = 7.5$ inches.
The area of the blueprint is 94.5 square inches.