The height of a tower is 200 m. A model of this tower is made such that the ratio between the height of the actual tower and that of the model is `160:1.` Find the height of the model.

Answer

To find the height of the model of the tower, we can follow these steps:

### Step 1: Understand the ratio
We know that the ratio of the height of the actual tower to the height of the model is given as 160:1. This means for every 160 units of height in the actual tower, there is 1 unit of height in the model.

### Step 2: Set up the equation
Let the height of the model be represented by \( x \). According to the ratio, we can write the equation as:
\[ \frac{200 \text{ m}}{x} = 160 \]

### Step 3: Cross-multiply to solve for \( x \)
Cross-multiplying gives us:
\[ 200 = 160x \]

### Step 4: Isolate \( x \)
To find \( x \), we divide both sides of the equation by 160:
\[ x = \frac{200}{160} \]

### Step 5: Simplify the fraction
Now, we simplify the fraction:
\[ x = \frac{200 \div 40}{160 \div 40} = \frac{5}{4} \]

### Step 6: Convert to decimal
To express \( \frac{5}{4} \) in decimal form:
\[ \frac{5}{4} = 1.25 \]

### Conclusion
Thus, the height of the model is:
\[ \text{Height of the model} = 1.25 \text{ m} \]

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