Question

practice proportional reasoning with scale drawings

1. model with mathematics martines town is building a volleyball court based on a scale drawing that is 40 centimeters by 80 centimeters and uses the scale 1 cm:22.5 cm.

a. write an equation for the proportional relationship between the scale drawings lengths ( x ) in centimeters and the actual courts lengths ( y ) in centimeters.

b. what are the length and width in meters of the actual court? show your work.

c. write the ratio of the area of the actual court to the area of the court in the scale drawing.

1. the students in robertos school are painting a mural that will be 8 feet by 15 feet. first they make a scale drawing of the mural with a scale of 2 feet:5 feet.

a. write an equation for the proportional relationship between the drawings lengths ( x ) in feet and the actual murals lengths ( y ) in feet.

b. what are the length and width of the scale drawing in feet? show your work.

c. open ended choose a different scale and use it to make a scale drawing of the mural that will fit on a piece of graph paper.

1. geography a map has a scale of 1 in.:10 mi. find the distance on the map between two cities that lie 147 miles apart. show your work.

Explanation:

Problem 1

Part A

Step1: Determine the proportion

Since the scale is \(1\) cm : \(22.5\) cm, for a proportional relationship \(y = kx\), where \(k\) is the constant of proportionality. Here \(k = 22.5\), so the equation is \(y=22.5x\)

Step1: Find the actual length and width in centimeters

For the scale drawing with \(x_1=40\) cm (width) and \(x_2 = 80\) cm (length). Using \(y=22.5x\)

• Width: \(y_1=22.5\times40=900\) cm
• Length: \(y_2=22.5\times80 = 1800\) cm

Step2: Convert centimeters to meters

Since \(1\) m \(= 100\) cm

• Width: \(y_1=\frac{900}{100}=9\) m
• Length: \(y_2=\frac{1800}{100}=18\) m

Step1: Calculate the area of the scale - drawing

\(A_{drawing}=40\times80=3200\) \(cm^{2}\)

Step2: Calculate the area of the actual court

\(A_{actual}=900\times1800 = 1620000\) \(cm^{2}\)

Step3: Find the ratio

\(\text{Ratio}=\frac{A_{actual}}{A_{drawing}}=\frac{1620000}{3200}=\frac{16200}{32}=\frac{2025}{4}\)

Answer:

\(y = 22.5x\)

Part B