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If the mean proportional of P and 125 is 100, then find the value of P.
77
80
79
82
80
Use the property of mean proportional: square the middle term (100) and divide by the known extreme (125). Thus, P = (100 ├Ч 100) / 125 = 10000 / 125 = 80.
Mean proportional of P and 125 is 100.
b=acтАЛтЯ╣b2=ac
Use the property of mean proportional: square the middle term (100) and divide by the known extreme (125). Thus, P = (100 ├Ч 100) / 125 = 10000 / 125 = 80.
Students often forget to square the mean proportional and instead divide 100 by 125, resulting in an incorrect fraction.
Define Mean Proportional
If 'b' is the mean proportional of 'a' and 'c', then the relationship is defined by a/b=b/c, or b2=ac.
b2=ac
Substitute Given Values
Here, a=P, b=100, and c=125. Plugging these into the formula: 1002=P├Ч125.
10000=125P
Calculate P
Solve for P by dividing both sides by 125: P=10000/125. Simplifying this gives 80.
P=80
B is correct because calculating the mean proportional 1002/125 results in 80.
This concept of mean proportional is identical to finding the 'Geometric Mean' of two numbers, which is a frequent concept in statistical data interpretation.
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