Question

a city planner creates a scaled map of a residential area. the actual area is defined by having a length of 800 meters and a width of 500 meters. using a scale factor of 0.02, what is the length of the scaled map?

a. 24 meters

b. 20 meters

c. 28 meters

d. 16 meters

if a building is 100 meters tall and you want to create a scale drawing using a scale factor of 0.1, what will be the height of the building in the scale drawing?

a. 5 meters

b. 10 meters

c. 8 meters

d. 12 meters

Explanation:

First Question (Scaled Map Length)

Step1: Recall scale factor formula

To find the scaled length, we use the formula: \( \text{Scaled Length} = \text{Actual Length} \times \text{Scale Factor} \)
The actual length is 800 meters and the scale factor is 0.02.

Step2: Calculate scaled length

Substitute the values into the formula: \( \text{Scaled Length} = 800 \times 0.02 \)
\( 800 \times 0.02 = 16 \)? Wait, no, wait. Wait, 800 0.02: 800 0.01 is 8, so 0.02 is 16? Wait, but let's check again. Wait, 800 0.02: 800 2 = 1600, then divide by 100: 16. But wait, the options: d is 16, but wait, maybe I misread the actual length? Wait, the problem says "actual area is defined by having a length of 800 meters" – wait, maybe it's a typo, but the question is about length. So actual length is 800m, scale factor 0.02. So 800 0.02 = 16? Wait, but let's check the options. Option d is 16 meters. Wait, but maybe I made a mistake. Wait, 800 0.02: 800 0.02 = 16. So the scaled length is 16 meters? Wait, but let's check again. Wait, 800 0.02: 800 * 2 = 1600, divided by 100 is 16. So yes.

Wait, but the options: a.24, b.20, c.28, d.16. So the answer should be d. 16 meters.

Step1: Recall scale factor formula

The formula for scaled height is: \( \text{Scaled Height} = \text{Actual Height} \times \text{Scale Factor} \)
Actual height is 100 meters, scale factor is 0.1.

Step2: Calculate scaled height

Substitute the values: \( \text{Scaled Height} = 100 \times 0.1 \)
\( 100 \times 0.1 = 10 \) meters.

Answer:

d. 16 meters

Second Question (Scaled Building Height)