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Sagot :
We have a scale for the drawing that is 1/4 inch = 2 feet.
This means that 1/4 inch in the drawing represent 2 feet in the real world.
1. Lobby.
The actual length is 16 feet.
If 2 feet are drawn in 1/4 inch (0.25), the drawing length is 2 inches
[tex]\frac{16*0.25}{2}=\frac{4}{2}=2[/tex]2. Principal's office
The drawing length is 1.25 inches.
We can calculate the actual length as:
[tex]1.25\cdot\frac{2}{0.25}=\frac{2.50}{0.25}=10[/tex]3. Library
The actual length is 20 feet.
We have discovered that we can transform this in drawing units (inches) multypling by 0.25/2=0.125.
[tex]20\cdot0.125=2.5[/tex]The drawing length is 2.5 inches.
4. School room
The drawing length is 3 inches.
We have discovered that we can transform this in actual length units by dividing by 0.125, or multiplying by 2/0.25=8:
[tex]3\cdot8=24[/tex]The actual length is 24 feet.
5. Science lab.
In the drawing has 1.5 inches, so we multiply by 8 and we get 1.5*8=12 feet.
The actual length is 12 feet.
6. Cafeteria
The actual length is 48 feet.
Then, the drawing length is 48*0.125=48/8=6 inches.
7. Music room
The drawing length is 4 inches.
Then, the actual length is 4*8=32 feet.
8. Gymnasium
The drawing length is 13 inches, so the actual length is 13*8=104 feet.
9. Auditorium
The actual length is 56 feet, so the drawing length is 56/8=7 inches.
10. Teachers lounge
The drawing length is 1.75 inches, so the actual length is 1.75*8=14 feet.
We can calculate the scale factor drawing to actual length as:
[tex]\frac{\text{drawing}}{\text{actual}}=\frac{\frac{1}{4}in}{2\text{ feet}}=\frac{1}{8}\cdot\frac{in}{\text{ feet}}\cdot\frac{1\text{ feet}}{12\text{ in}}=\frac{1}{96}[/tex]The scale is 1:96.
12) If the scale is 12 inches = 1 foot, the scale factor is:
[tex]\frac{\text{drawing length}}{\text{actual length}}=\frac{12\text{ in}}{1\text{ ft}}\cdot\frac{1\text{ ft}}{12\text{ in}}=1[/tex]The scale in this case is 1:1 (the drawing has the same size as the actual object).
14) We have a road which length is 30 cm.
The scale is 1 cm = 3.5 m.
We can calculate the actual length of the road as:
[tex]\text{Actual length}=30cm\cdot\frac{3.5\text{ m}}{1\text{ cm}}=105\text{ m}[/tex]The actual legth of the road is 105 meters.
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