If the fourth proportional to P, 22 and 8 is 11, then find the value of P.
16
To solve this problem, we need to find the fourth proportional to the numbers \( P \), 22, and 8, given that it is 11. The concept of proportion involves four numbers \( a, b, c, \) and \( d \) such that \( a:b = c:d \). Here, \( d \) is the fourth proportional.
The relationship can be expressed as:
\frac{P}{22} = \frac{8}{11}
We can solve for \( P \) by cross-multiplying:
- Multiply both sides by 22 to eliminate the fraction:
- P \times 11 = 22 \times 8
- Calculate the right side:
- 22 \times 8 = 176
- Thus, the equation becomes:
- 11P = 176
- Solve for \( P \) by dividing both sides by 11:
- P = \frac{176}{11} = 16
Therefore, the value of \( P \) is 16.
This matches option 16, confirming it as the correct answer.
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