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The fourth proportional to 18, a and 8a is 16. What is the positive value of a?
Question

The fourth proportional to 18, a and 8a is 16. What is the positive value of a?

A.

6

B.

9

C.

3

D.

8

Correct option is A

Given
First term = 18
Second term = a
Third term = 8a
Fourth proportional = 16
Formula Used
For proportional terms  x, y, z, w: xy=zw\frac{x}{y} = \frac{z}{w}
Solution
According to the property of proportion:
18a=8a16 18a=a2 a2=18×2 a2=36 a=36=6 \frac{18}{a} = \frac{8a}{16} \\\ \\\frac{18}{a} = \frac{a}{2} \\\ \\a^2 = 18 × 2 \\\ \\a^2 = 36 \\\ \\a = \sqrt{36} = 6 \\\ \\​​
Final Answer
So the correct answer is (a)

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