problems 2 - 4: leonardo da vincis famous painting, the mona lisa, measures 21 inches by 30 inches.
2. create a scale drawing of the outline of the mona lisa where 1 unit represents 3 inches.
3. create a scale drawing of the outline of the mona lisa where 2 units represents 5 inches.
4. imagine a new scale drawing of the mona lisa where 3 units represent 1 inch. is this drawing smaller, larger, or equal in size compared to your previous drawings? explain your thinking.
5. the floor - plan of a restaurant shows a scale of 1 inch to 12 feet. the floor - plan shows the area of the restaurant as 60 square inches. hoang says the actual area of the restaurant is 720 square feet. is hoang correct? explain your thinking.

Question

Accepted Answer

### Problem 2
# Explanation:
## Step1: Calculate width in scale - units
The actual width of the Mona Lisa is 21 inches. Since 1 unit represents 3 inches, the number of units for the width is $\frac{21}{3}=7$ units.
## Step2: Calculate height in scale - units
The actual height of the Mona Lisa is 30 inches. Since 1 unit represents 3 inches, the number of units for the height is $\frac{30}{3}=10$ units.
# Answer:
The scale - drawing should be 7 units wide and 10 units high.

### Problem 3
# Explanation:
## Step1: Calculate width in scale - units
The actual width of the Mona Lisa is 21 inches. Since 2 units represent 5 inches, the number of units for the width is $21\div\frac{5}{2}=21	imes\frac{2}{5}=8.4$ units.
## Step2: Calculate height in scale - units
The actual height of the Mona Lisa is 30 inches. Since 2 units represent 5 inches, the number of units for the height is $30\div\frac{5}{2}=30	imes\frac{2}{5}=12$ units.
# Answer:
The scale - drawing should be 8.4 units wide and 12 units high.

### Problem 4
# Explanation:
## Step1: Analyze the scale of previous drawings
In problem 2, 1 unit represents 3 inches. In problem 3, 2 units represent 5 inches (1 unit represents 2.5 inches).
## Step2: Analyze the new scale
In the new scale, 3 units represent 1 inch (1 unit represents $\frac{1}{3}$ inch).
## Step3: Compare the scales
Since $\frac{1}{3}<2.5$ and $\frac{1}{3}<3$, more units are needed to represent the same actual - length in the new scale. So the new drawing is larger.
# Answer:
The new drawing is larger because in the new scale, 1 unit represents $\frac{1}{3}$ inch, which is a smaller length compared to the units in the previous scales (1 unit represented 3 inches in problem 2 and 2.5 inches in problem 3), so more units are needed to represent the same actual dimensions of the Mona Lisa.

### Problem 5
# Explanation:
## Step1: Find the linear - scale factor
The linear - scale factor is 1 inch represents 12 feet. So the area - scale factor is $(12)^2$ because area is a two - dimensional measurement.
## Step2: Calculate the actual area
The area on the floor - plan is 60 square inches. The actual area $A$ is $A = 60	imes(12)^2=60	imes144 = 8640$ square feet.
## Step3: Check Hoang's answer
Hoang says the actual area is 720 square feet. Since $720
eq8640$, Hoang is incorrect.
# Answer:
Hoang is incorrect. The actual area of the restaurant is 8640 square feet. The area - scale factor is the square of the linear - scale factor. The linear - scale factor is 12 (1 inch represents 12 feet), so the area - scale factor is 144, and the actual area is $60	imes144 = 8640$ square feet.

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QUESTION IMAGE

Question

Explanation:

Problem 2

Step1: Calculate width in scale - units

Step2: Calculate height in scale - units

Step1: Calculate width in scale - units

Step2: Calculate height in scale - units

Step1: Analyze the scale of previous drawings

Step2: Analyze the new scale

Step3: Compare the scales

Answer:

Problem 3