Certainly! Let's break this down step by step:
1. Understand the Ratio:
- The height increase is given in the ratio 2:3.
- This means that for every 2 units of the studut's current height, we expect it to increase to 3 units.
2. Identify the Current Height:
- The current height of the student is given as 140 cm.
3. Apply the Ratio:
- To find the new height, we use the ratio to determine the factor by which the height increases.
- The ratio of old height to new height is 2:3. So, if we let the old height be `2x`, the new height would then be `3x`.
4. Set Up the Proportion:
- Given the current height is 140 cm (which corresponds to the `2` parts in the ratio), we can set up a proportion:
[tex]\[
\frac{\text{Current Height}}{2} = \frac{\text{New Height}}{3}
\][/tex]
- Plugging in the current height, we get:
[tex]\[
\frac{140}{2} = \frac{\text{New Height}}{3}
\][/tex]
5. Solve for the New Height:
- First, calculate the factor for the current height:
[tex]\[
140 \div 2 = 70
\][/tex]
- This means one part of the ratio corresponds to 70 cm.
- Since the new height corresponds to 3 parts, multiply 70 by 3 to get the new height:
[tex]\[
70 \times 3 = 210 \text{ cm}
\][/tex]
6. Conclusion:
- Therefore, the new height of the student is 210 cm.
So the new height, considering the given ratio, is [tex]\( \boxed{210 \text{ cm}} \)[/tex].
