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Finding the Third Proportional to 189.84 and 284.77

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Solution

The third proportional to 189.84 and 284.77 is: 427.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    189.84 : 284.77 = 284.77 : x
  2. Step 2: Convert to fraction form
    189.84/284.77 = 284.77/x
  3. Step 3: Cross multiply
    189.84x = 284.77 × 284.77
  4. Step 4: Simplify right side
    189.84x = 81,091.46
  5. Step 5: Solve for x
    x = 81,091.46/189.84
  6. Step 6: Final answer
    x = 427.15

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.