Question

study the example showing how to use a scale drawing to find actual measurements. then solve problems 1 - 7.
example
an architect drew a scale drawing of a new art museum on centimeter grid paper. each centimeter on the drawing represents 5 meters in the actual museum. what are the length and width of the sculpture room in the museum?
the sculpture room in the drawing is 6 centimeters long and 2 centimeters wide. the scale is 1 cm : 5 m. one way to solve the problem is to use the scale to make a table of equivalent ratios.

distance on the scale drawing (cm)	1	2	3	4	5	6
distance in the museum (m)	5	10	15	20	25	30

the table shows, the length of the actual room is 30 meters and the width is 10 meters.

1. you can also write an equation for equivalent ratios. the equation at the right can be used to find the actual length x of the sculpture room in the museum. complete the equation and explain what each part represents.

1. how can you use the equation to find the actual length of the sculpture room?

1. write and solve an equation to find the actual width of the sculpture room.

vocabu
scale drawing: drawing that shows an object with measurements in proportion to the measurements of the actual object.
scale: a ratio that compares the measurements of a scale drawing to the actual measurements.

Explanation:

Step1: Set up the proportion for length

The scale is 1 cm represents 5 m. For the length of the sculpture - room, if the length on the scale - drawing is 6 cm and the actual length is \(x\) meters, the proportion is \(\frac{1\ cm}{5\ m}=\frac{6\ cm}{x\ m}\). Here, 1 cm is the unit distance on the scale - drawing, 5 m is the corresponding actual distance, 6 cm is the length of the sculpture room on the scale - drawing, and \(x\) is the unknown actual length.

Step2: Solve the proportion for length

Cross - multiply the proportion \(\frac{1}{5}=\frac{6}{x}\) to get \(1\times x = 5\times6\), so \(x = 30\) m.

Step3: Set up the proportion for width

Let the actual width be \(y\) meters. The width on the scale - drawing is 2 cm. The proportion is \(\frac{1\ cm}{5\ m}=\frac{2\ cm}{y\ m}\). Here, 1 cm is the unit distance on the scale - drawing, 5 m is the corresponding actual distance, 2 cm is the width of the sculpture room on the scale - drawing, and \(y\) is the unknown actual width.

Step4: Solve the proportion for width

Cross - multiply the proportion \(\frac{1}{5}=\frac{2}{y}\) to get \(1\times y=5\times2\), so \(y = 10\) m.

Answer:

1. The equation for the length is \(\frac{1\ cm}{5\ m}=\frac{6\ cm}{x\ m}\), where 1 cm is the unit distance on the scale - drawing, 5 m is the actual distance corresponding to 1 cm on the scale - drawing, 6 cm is the length of the sculpture room on the scale - drawing, and \(x\) is the actual length of the sculpture room.
2. Cross - multiply the proportion \(\frac{1}{5}=\frac{6}{x}\) (from the length equation) to find \(x\). \(1\times x = 5\times6\), so \(x = 30\) m.
3. The equation for the width is \(\frac{1\ cm}{5\ m}=\frac{2\ cm}{y\ m}\). Cross - multiply: \(1\times y = 5\times2\), so \(y = 10\) m. The actual width of the sculpture room is 10 m.