Sure, let's solve this step-by-step:
1. Understand the given information:
- The initial height of the object (or the student, in this case) is 140 cm.
- The ratio of the height increase is 2:3.
2. What does the ratio 2:3 mean?
- The ratio 2:3 implies that for every 2 parts of the initial height, the new height will be 3 parts. Essentially, the height is scaling by a factor that can be derived from this ratio.
3. Calculate the scaling factor:
- Given the ratio 2:3, we can determine that the new height is (3/2) times the initial height.
4. Use the scaling factor to find the new height:
- The initial height is 140 cm.
- The new height is obtained by multiplying the initial height by the scaling factor (3/2).
So, multiplying the initial height by the scaling factor:
[tex]\[ \text{New Height} = 140 \, \text{cm} \times \frac{3}{2} \][/tex]
Solving this will give us:
[tex]\[ \text{New Height} = 210 \, \text{cm} \][/tex]
Therefore, the new height of the student is 210 cm.
