Sure, let's tackle these two parts step-by-step.
### Part a: The length of the real car
#### Given:
- The length of the model car = 40 cm
- The scale factor of the model car to the real car = 1/10 (or 0.1)
#### To find:
- The length of the real car
#### Solution:
The model car is scaled down by a factor of 1/10 compared to the real car. Therefore, to find the length of the real car, we need to multiply the length of the model car by the reciprocal of the scale factor (which is 10 in this case).
[tex]\[
\text{Length of the real car} = \text{Length of the model car} \times \frac{1}{\text{Scale factor}}
\][/tex]
[tex]\[
\text{Length of the real car} = 40 \, \text{cm} \times 10
\][/tex]
[tex]\[
\text{Length of the real car} = 400 \, \text{cm}
\][/tex]
So, the length of the real car is 400 cm.
### Part b: The height of the model car
#### Given:
- The height of the real car = 150 cm
- The scale factor of the model car to the real car = 1/10 (or 0.1)
#### To find:
- The height of the model car
#### Solution:
The real car is scaled down by a factor of 1/10 to get the model car. Therefore, to find the height of the model car, we need to multiply the height of the real car by the scale factor.
[tex]\[
\text{Height of the model car} = \text{Height of the real car} \times \text{Scale factor}
\][/tex]
[tex]\[
\text{Height of the model car} = 150 \, \text{cm} \times 0.1
\][/tex]
[tex]\[
\text{Height of the model car} = 15 \, \text{cm}
\][/tex]
So, the height of the model car is 15 cm.
### Summary:
a. The length of the real car is 400 cm.
b. The height of the model car is 15 cm.
