Question

On a set of architectural drawings for a new school building the scale is 1/4 inch = 2 feet. Find the missing lengths of the rooms.

Answer 1

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

`(16*0.25)/(2)=(4)/(2)=2`

2. Principal's office

The drawing length is 1.25 inches.

We can calculate the actual length as:

`1.25\cdot(2)/(0.25)=(2.50)/(0.25)=10`

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.

`20\cdot0.125=2.5`

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:

`3\cdot8=24`

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:

`\frac{\text{drawing}}{\text{actual}}=\frac{(1)/(4)in}{2\text{ feet}}=(1)/(8)\cdot\frac{in}{\text{ feet}}\cdot\frac{1\text{ feet}}{12\text{ in}}=(1)/(96)`

The scale is 1:96.

12) If the scale is 12 inches = 1 foot, the scale factor is:

`\frac{\text{drawing length}}{\text{actual length}}=\frac{12\text{ in}}{1\text{ ft}}\cdot\frac{1\text{ ft}}{12\text{ in}}=1`

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:

`\text{Actual length}=30cm\cdot\frac{3.5\text{ m}}{1\text{ cm}}=105\text{ m}`

The actual legth of the road is 105 meters.