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If 14.
.7 and x > 0, then find the value of x.
7.4
1
12.9
11.4
7.4
For any proportion a:x:: x:b, x is the mean proportional, which is calculated as the square root of the product of the extremes (x = sqrt(a * b)).
For any proportion a:x:: x:b, x is the mean proportional, which is calculated as the square root of the product of the extremes (x = sqrt(a * b)).
Establish the relationship
In the proportion 14.
.7, the product of the means equals the product of the extremes: x * x = 14.8 * 3.7.
Calculate the product
Calculate 14.8 * 3.7: 14.8 * 3 = 44.4 and 14.8 * 0.7 = 10.36. Adding them gives 44.4 + 10.36 = 54.76.
Find the square root
To find x, calculate the square root of 54.76. Since 7 * 7 = 49 and 8 * 8 = 64, and the last digit is 6, the root is 7.4.
B: 4.1 squared is 16.81, which does not match 54.76. C: 12.9 squared is 166.41, far exceeding 54.76. D: 11.4 squared is 129.96, which is incorrect.
A is correct because 7.4 squared equals 54.76, which is the exact product of 14.8 and 3.7 as required by the mean proportional property.
When dealing with mean proportionals involving decimals, estimate the range first (e.g., 14 * 4 = 56, so the result must be close to sqrt(56) which is between 7 and 8) to eliminate obviously wrong options.
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