High School

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To find the scale of a drawing or model:

1. Write the ratio of the model length to the actual length.
2. Simplify the ratio so the numerator is 1. (Divide the numerator and denominator by the numerator.)

Directions: Find the scale for each drawing/model.

1. **Model Height:** 6 in
**Actual Height:** 72 ft

2. A poster was made of a 6-foot tall musician. If the musician on the poster is 20 inches tall, what was the scale used to make the poster?

3. **Map Distance:** 36 cm
**Actual Distance:** [tex]$4 \frac{1}{2} \, \text{km}$[/tex]

4. A model airplane is 18 centimeters long. If the actual airplane is 60 meters long, what scale was used to create the model?

Answer :

Sure, let's go through each problem step-by-step to find the scale for each drawing or model.

### Problem 9:
Model Height: 6 inches
 Actual Height: 72 feet

First, we need to convert the actual height from feet to inches because the model height is given in inches.

1 foot = 12 inches

So, 72 feet = 72 12 = 864 inches

Now, write the ratio of the model height to the actual height:
[tex]\[ \frac{6 \text{ in}}{864 \text{ in}} \][/tex]

We simplify this ratio by dividing the numerator and the denominator by the numerator (6):

[tex]\[ \frac{6 \div 6}{864 \div 6} = \frac{1}{144} \][/tex]

So, the scale for this model is 1:144.

### Problem 11:
 Actual Height of Musician: 6 feet
Height on Poster: 20 inches

First, convert the actual height from feet to inches:

6 feet = 6 12 = 72 inches

Now, write the ratio of the poster height to the actual height:
[tex]\[ \frac{20 \text{ in}}{72 \text{ in}} \][/tex]

We simplify this ratio by dividing both the numerator and the denominator by the numerator (20):

[tex]\[ \frac{20 \div 20}{72 \div 20} = \frac{1}{3.6} \][/tex]

So, the scale used to make the poster is 1:3.6.

### Problem 10:
Map Distance: 36 cm
 Actual Distance: [tex]\( 4 \frac{1}{2} \)[/tex] km

First, convert the actual distance from kilometers to centimeters:

1 kilometer = 1000 meters
1 meter = 100 centimeters

So, [tex]\( 4.5 \)[/tex] kilometers = [tex]\( 4.5 \times 1000 \times 100 = 450000 \)[/tex] centimeters

Now, write the ratio of the map distance to the actual distance:
[tex]\[ \frac{36 \text{ cm}}{450000 \text{ cm}} \][/tex]

We simplify this ratio by dividing both the numerator and the denominator by the numerator (36):

[tex]\[ \frac{36 \div 36}{450000 \div 36} = \frac{1}{12500} \][/tex]

So, the scale for this map is 1:12500.

### Problem 12:
Model Airplane Length: 18 cm
 Actual Airplane Length: 60 meters

First, convert the actual length from meters to centimeters:

1 meter = 100 centimeters

So, 60 meters = 60 * 100 = 6000 centimeters

Now, write the ratio of the model airplane length to the actual airplane length:
[tex]\[ \frac{18 \text{ cm}}{6000 \text{ cm}} \][/tex]

We simplify this ratio by dividing both the numerator and the denominator by the numerator (18):

[tex]\[ \frac{18 \div 18}{6000 \div 18} = \frac{1}{333.3333333333333} \][/tex]

So, the scale used to create the model airplane is approximately 1:333.33.

To summarize:
- Problem 9: Scale is 1:144
- Problem 11: Scale is 1:3.6
- Problem 10: Scale is 1:12500
- Problem 12: Scale is approximately 1:333.33

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Rewritten by : Barada