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If the mean proportional of P and 100 is 50, then find the value of P.
25
28
22
24
25
Since the mean proportional is 50, the product of the two numbers is 502=2500. If one number is 100, divide 2500 by 100 to get P.
Mean proportional of P and 100 is 50.
b=acтАЛтЯ╣b2=ac
Since the mean proportional is 50, the product of the two numbers is 502=2500. If one number is 100, divide 2500 by 100 to get P.
Many students mistake 'mean proportional' for the arithmetic mean (average) and calculate (P+100)/2=50, which is incorrect.
Define Mean Proportional
If b is the mean proportional of a and c, then a/b=b/c, which simplifies to b2=ac.
b2=ac
Substitute Known Values
Here, a=P, b=50, and c=100. Substituting these into the formula: 502=P├Ч100.
502=P├Ч100
Solve for P
Calculate the square: 2500=P├Ч100. Divide both sides by 100 to isolate P.
P=1002500тАЛ=25
A is correct because the mean proportional 502/100 results in 2500/100=25.
This concept is a specific case of geometric mean; it frequently appears in questions involving finding a third side in similar triangles or scale factor problems in geometry.
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