If A and B are in the ratio 4 : 5 and the difference of

If A and B are in the ratio 4 : 5 and the difference of their squares is 81, what is the value of A ?

Let A = 4x and B = 5x.
According to the question,
(5x)² – (4x)² 81
⇒ 25x² – 16x² = 81
⇒ 9x² = 81 ⇒ x² = 9
⇒ x = √9 = 3
∴ A = 4x = 4 × 3 = 12