The sum of the fourth proportional of 4, 5, 16 and the mean proportional of 4, 16, is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 28
The fourth proportional of \(a\), \(b\), \(c\) is the number \(x\) with \(a:b=c:x\). The mean proportional of \(a\) and \(b\) is the number \(m\) with \(a:m=m:b\), that is, \(m=\sqrt{ab}\).
Fourth proportional of 4, 5, 16: \(4:5=16:x\), so \(\displaystyle x=\frac{5\times16}{4}=20\)
Mean proportional of 4 and 16: \(m=\sqrt{4\times16}=\sqrt{64}=8\)
Sum \(=20+8=28\)