Question

1. art marie has a small copy of rene magrittes famous painting, the schoolmaster. her copy has dimensions 2 inches by 1.5 inches. the scale of the copy is 1 in:40 cm.

a. find the dimensions of the original painting.
b. find the area of the original painting.
c. since 1 inch is 2.54 centimeters, find the dimensions of the original painting in inches.
d. find the area of the original painting in square inches.

1. a game room has a floor that is 120 feet by 75 feet. a scale drawing of the floor on grid paper uses a scale of 1 unit:5 feet. what are the dimensions of the scale drawing?
2. multiple representations the length of a table is 6 feet. on a scale drawing, the length is 2 inches. write three possible scales for the drawing.
3. analyze relationships a scale for a scale drawing is 10 cm:1 mm. which is larger, the actual object or the scale drawing? explain.
4. architecture the scale model of a building is 5.4 feet tall.

a. if the original building is 810 meters tall, what was the scale used to make the model?
b. if the model is made out of tiny bricks each measuring 0.4 inch in height, how many bricks tall is the model?

Explanation:

Problem 6

Step1: Convert copy dims to original (cm)

Original length: $2 \times 40 = 80$ cm
Original width: $1.5 \times 40 = 60$ cm

Step2: Calculate area (cm²)

$\text{Area} = 80 \times 60 = 4800$ cm²

Step3: Convert original dims to inches

Length in inches: $\frac{80}{2.54} \approx 31.50$ inches
Width in inches: $\frac{60}{2.54} \approx 23.62$ inches

Step4: Calculate area (in²)

$\text{Area} = 31.50 \times 23.62 \approx 744.03$ in²

Step1: Convert floor dims to drawing units

Length: $\frac{120}{5} = 24$ units
Width: $\frac{75}{5} = 15$ units

Step1: Simplify base scale (in:ft)

Base scale: 2 in : 6 ft = 1 in : 3 ft

Step2: Convert to in:in scale

$3 \text{ ft} = 36 \text{ in}$, so 1 in : 36 in

Step3: Expand to equivalent scale

Multiply both sides by 2: 2 in : 72 in (or 2 in : 6 ft, same as original)

Answer:

a. 80 cm by 60 cm
b. 4800 square centimeters
c. ~31.50 inches by ~23.62 inches
d. ~744.03 square inches

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Problem 7