Question:
The fourth proportional to 4, a and 16a is 81. What is the value of a?
4, a और 16a का चौथा समानुपाती 81 है। a का मान क्या है?
Options:
- a) 13/2
- b) 5/2
- c) 9/2
- d) 11/2
- a) 13/2
- b) 5/2
- c) 9/2
- d) 11/2
correct answer : c)
Explanation:
The fourth proportional to \(4\), \(a\), and \(16a\) is \(81\).
Therefore, \(\frac{4}{a} = \frac{16a}{81}\)
\(16a^2 = 324\)
\(a^2 = \frac{324}{16} = \frac{81}{4}\)
\(a = \frac{9}{2}\).
\(4\), \(a\), और \(16a\) का चौथा समानुपाती \(81\) है।
इसलिए, \(\frac{4}{a} = \frac{16a}{81}\)
\(16a^2 = 324\)
\(a^2 = \frac{324}{16} = \frac{81}{4}\)
\(a = \frac{9}{2}\).