Question

Emily wants to draw a plan of her room on a piece of paper measuring 16 cm x 20 cm. If the area of the room is 3.5 m x 4.5 m, which scale is appropriate to use to draw the plan?

A) 1 : 1/20
B) 1 : 1/25
C) 1 : 20
D) 1 : 25​

Answer 1

To find the appropriate scale to use for drawing the room plan, we need to compare the dimensions of the paper to the actual dimensions of the room.

Given:

Paper dimensions: 16 cm x 20 cm

Room dimensions: 3.5 m x 4.5 m

First, we need to convert the room dimensions to the same unit as the paper dimensions. Since 1 meter = 100 centimeters, we have:

Room dimensions: 350 cm x 450 cm

Now, let's compare the dimensions of the paper and the room:

Paper width: 16 cm

Room width: 350 cm

Paper length: 20 cm

Room length: 450 cm

To find the appropriate scale, we'll use the formula: Scale = Length (or Width) on paper / Length (or Width) in real life

For width:

Scale = 16 cm / 350 cm ≈ 0.0457

For length:

Scale = 20 cm / 450 cm ≈ 0.0444

Since the scale values are very close to each other, we can take an average to get an approximate scale:

Average Scale ≈ (0.0457 + 0.0444) / 2 ≈ 0.04505

Now, let's check the answer choices and find the one that is closest to our calculated average scale:

A) 1 : 1/20 ≈ 0.05 (not a close match)

B) 1 : 1/25 = 0.04 (not a close match)

C) 1 : 20 = 0.05 (close match)

D) 1 : 25 = 0.04 (not a close match)

The closest match is option C) 1 : 20, which has a scale of 0.05. Therefore, the appropriate scale to use to draw the room plan is 1 : 20.