Question

a bridge is 1200 meters long and is being scaled down by a factor of 0.02 for a model. what will be the length of the model bridge?
a. 28 meters
b. 15 meters
c. 32 meters
d. 24 meters

if a triangle is dilated by a scale factor of 2, what happens to the side lengths?
a. they are halved
b. they remain the same
c. they triple in size
d. they double in size

a rectangular park is 600 meters long and 400 meters wide. using a scale factor of 0.05, what will be the width of the scaled-down park?
a. 10 meters
b. 30 meters
c. 20 meters
d. 40 meters

Explanation:

First Question:

Step1: Identify the formula for scaling

To find the length of the model bridge, we use the formula: \( \text{Model Length} = \text{Actual Length} \times \text{Scale Factor} \)

Step2: Substitute the given values

The actual length of the bridge is \( 1200 \) meters and the scale factor is \( 0.02 \). So, \( \text{Model Length} = 1200 \times 0.02 \)

Step3: Calculate the result

\( 1200 \times 0.02 = 24 \) meters

Dilation is a transformation that changes the size of a figure. When a figure is dilated by a scale factor, the side lengths of the figure are multiplied by that scale factor. If the scale factor is 2, each side length is multiplied by 2, meaning they double in size.

Step1: Identify the formula for scaling

To find the width of the scaled - down park, we use the formula: \( \text{Scaled - down Width} = \text{Actual Width} \times \text{Scale Factor} \)

Step2: Substitute the given values

The actual width of the park is \( 400 \) meters and the scale factor is \( 0.05 \). So, \( \text{Scaled - down Width}=400\times0.05 \)

Step3: Calculate the result

\( 400\times0.05 = 20 \) meters

Answer:

d. 24 meters

Second Question: