The fourth proportion to 12,24 and 27 is the same as the third proportion to A and 36 . What is the value of A?

22 24 26 20

24

Using direct formula for the fourth proportional,  d = \(\frac{b\; \times\; c}{a}\)    = \(\frac{24\; \times\; 27}{12}\) = 54 The third proportional of A and 36 is 54 Third proportional is = c = \(\frac{b^2}{a}\) ⇒ 54 =  \(\frac{36^2}{A}\) ⇒ A =  \(\frac{36 × 36}{54}\) ⇒ A = 24