If 54: A :: A: 150, then find the positive value of A.
Solving for 'A' in a Proportion
The problem presents a proportion: 54 : A :: A : 150. We need to find the positive value of A.
Understanding Proportions
A proportion is an equation stating that two ratios are equal. The given proportion can be written as:
$ \frac{54}{A} = \frac{A}{150} $
Calculating the Value of A
To solve for A, we cross-multiply:
$ A \times A = 54 \times 150 $
This simplifies to:
$ A^2 = 54 \times 150 $
Calculate the product:
$ A^2 = 8100 $
Now, find the positive square root of 8100 to get the value of A:
$ A = \sqrt{8100} $
$ A = 90 $
Therefore, the positive value of A is 90.
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