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. 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. 2 how can you use the equation to find the actual length of the sculpture room? 3 write and solve an equation to find the actual width of the sculpture room. vocabulary: scale drawing: a drawing that shows an object with its measurements in proportion to the actual measurements of the object. scale: a ratio that compares the measurements used in a scale drawing with the actual measurements.

Explanation:

Step1: Set up proportion for length

The scale is 1 cm represents 5 m. For the length of the sculpture - room which is 6 cm on the drawing. Let the actual length be $x$ meters. The proportion is $\frac{1}{5}=\frac{6}{x}$. Here, 1 is the distance on the scale - drawing in cm, 5 is the corresponding actual distance in m, 6 is the length of the room on the scale - drawing in cm, and $x$ is the actual length of the room in m.

Step2: Solve for $x$ (length)

Cross - multiply the proportion $\frac{1}{5}=\frac{6}{x}$: $1\times x = 5\times6$. So, $x = 30$ meters.

Step3: Set up proportion for width

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

Step4: Solve for $y$ (width)

Cross - multiply the proportion $\frac{1}{5}=\frac{2}{y}$: $1\times y=5\times2$. So, $y = 10$ meters.

Answer:

1. The equation for the length is $\frac{1}{5}=\frac{6}{x}$, where 1 is the distance on the scale - drawing (in cm), 5 is the actual distance corresponding to 1 cm on the scale - drawing (in m), 6 is the length of the room on the scale - drawing (in cm), and $x$ is the actual length of the room (in m).
2. To find the actual length, cross - multiply the proportion $\frac{1}{5}=\frac{6}{x}$ to get $x = 30$ meters.
3. The equation for the width is $\frac{1}{5}=\frac{2}{y}$, where 1 is the distance on the scale - drawing (in cm), 5 is the actual distance corresponding to 1 cm on the scale - drawing (in m), 2 is the width of the room on the scale - drawing (in cm), and $y$ is the actual width of the room (in m). Solving for $y$ by cross - multiplying gives $y = 10$ meters.