Consider the following statements:
I. The fourth proportional to 4, 6 and 10 is 12.
II. The mean proportional between 9 and 16 is 12.
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Only II
If \(a:b=c:d\), then \(d=\displaystyle\frac{bc}{a}\) is the fourth proportional; the mean proportional between \(a\) and \(b\) is \(\sqrt{ab}\).
I. The fourth proportional to 4, 6 and 10 is 12. — Incorrect. The fourth proportional is 15.
\(4:6=10:d\)
\(d=\displaystyle\frac{6\times10}{4}=15\)
II. The mean proportional between 9 and 16 is 12. — Correct. \(12^2=144=9\times16\).
\(\sqrt{9\times16}=\sqrt{144}=12\)
Check: \(9:12=12:16\), both equal to \(3:4\)