Find the fourth proportional to 7 . 2, 1. 8, 8 . 4

Answer

To find the fourth proportional to the numbers 7.2, 1.8, and 8.4, we can follow these steps:

### Step 1: Understand the concept of fourth proportional
The fourth proportional to three numbers \( a, b, c \) is a number \( x \) such that the ratio of \( a \) to \( b \) is the same as the ratio of \( c \) to \( x \). This can be expressed as:
\[ \frac{a}{b} = \frac{c}{x} \]

### Step 2: Assign the values
In this case, we have:
- \( a = 7.2 \)
- \( b = 1.8 \)
- \( c = 8.4 \)
- \( x = ? \) (the fourth proportional)

### Step 3: Set up the proportion
Using the relationship from Step 1, we can write:
\[ \frac{7.2}{1.8} = \frac{8.4}{x} \]

### Step 4: Cross-multiply to solve for \( x \)
Cross-multiplying gives us:
\[ 7.2 \cdot x = 1.8 \cdot 8.4 \]

### Step 5: Calculate \( 1.8 \cdot 8.4 \)
Calculating the right side:
\[ 1.8 \cdot 8.4 = 15.12 \]

### Step 6: Substitute back into the equation
Now we have:
\[ 7.2 \cdot x = 15.12 \]

### Step 7: Solve for \( x \)
To find \( x \), divide both sides by 7.2:
\[ x = \frac{15.12}{7.2} \]

### Step 8: Perform the division
Calculating the division:
\[ x = 2.1 \]

### Conclusion
The fourth proportional to 7.2, 1.8, and 8.4 is \( 2.1 \).

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