Understanding the Height Ratio Problem

This question asks us to find the height of Nani given the ratio of the heights of Nani and Leelu, and the actual height of Leelu. We are told the ratio of Nani's height to Leelu's height is 4:3. This means for every 4 units of height Nani has, Leelu has 3 units of height.

The given information is:

• Ratio of Nani's height : Leelu's height = 4 : 3
• Leelu's height = 1.2 m

We need to find Nani's height.

Setting up the Calculation using Ratio

A ratio of 4:3 can be written as a fraction $\frac{4}{3}$. The ratio of Nani's height to Leelu's height is equal to this fraction. Let $H_N$ be the height of Nani and $H_L$ be the height of Leelu.

The ratio can be expressed as:

$\frac{H_N}{H_L} = \frac{4}{3}$

We are given that $H_L = 1.2$ m. We can substitute this value into the equation:

$\frac{H_N}{1.2} = \frac{4}{3}$

Calculating Nani's Height

Now, we need to solve this equation for $H_N$. To isolate $H_N$, we can multiply both sides of the equation by 1.2:

$H_N = \frac{4}{3} \times 1.2$

We can perform the multiplication:

$H_N = \frac{4 \times 1.2}{3}$

$H_N = \frac{4.8}{3}$

Now, divide 4.8 by 3:

$H_N = 1.6$

So, the height of Nani is 1.6 meters.

Let's quickly check if the ratio of Nani's height (1.6 m) to Leelu's height (1.2 m) is indeed 4:3:

Ratio = $\frac{1.6}{1.2} = \frac{16}{12}$ (Multiplying numerator and denominator by 10)

Simplifying the fraction by dividing both by their greatest common divisor, which is 4:

$\frac{16 \div 4}{12 \div 4} = \frac{4}{3}$

The ratio is indeed 4:3, confirming our calculated height for Nani is correct.

Summary of Height Calculation

Here is a summary of the steps taken to find Nani's height based on the given height ratio:

Revision Table: Key Concepts

Additional Information on Ratios and Proportions

Ratios and proportions are fundamental concepts in mathematics used to compare quantities and solve problems involving scaling. A ratio gives us a relative comparison, while a proportion allows us to find unknown values when two ratios are equivalent.

• Units: When working with ratios, ensure the quantities being compared are in the same units. In this problem, both heights are in meters, so the units cancel out in the ratio, and the result for Nani's height will also be in meters.
• Direct Proportion: In this case, Nani's height and Leelu's height are in direct proportion. If one height increases, the other height increases proportionally, maintaining the same ratio.
• Applications: Ratios and proportions are used in many real-world situations, such as scaling recipes, mixing paint, reading maps, and comparing speeds.

The final answer is 1.6 m.