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If 25:x::x:36, and x>0, then what is the value of x?
21
18
27
30
30
For any proportion of the form a : x :: x : b, the value of x is the mean proportional, calculated as the square root of (a times b).
For any proportion of the form a : x :: x : b, the value of x is the mean proportional, calculated as the square root of (a times b).
Set up the proportion equation
The given expression 25 : x :: x : 36 is a proportion, which means the ratio 25/x is equal to x/36.
Apply cross-multiplication
Multiplying the extremes and the means gives x * x = 25 * 36, which simplifies to x squared = 900.
Solve for x
Taking the square root of 900 (given x > 0), we find x = 30.
A: 21 squared is 441, not 900. B: 18 squared is 324, not 900. C: 27 squared is 729, not 900.
D is correct because the geometric mean of 25 and 36 is the square root of 900, which equals 30.
When faced with a: b:: b: c, always remember the shortcut x = square root of (a * c) to save time on exams.
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