Question

two numbers are in the ratio 4:5.the difference of their squares is 81. find the numbers

Answer 1

Let,
x/y = 4/5 
y^2 - x^2 = 81 

x = 4y/5 
y^2 - (4y/5)^2 = 81 
y^2 - 16y^2/25 = 81 
9y^2/25 = 81 
y = sqrt (81*25/9) 
y = 15 

x = 4(15)/5 = 12

Answer 2

Let the numbers be 4x and 5x.

(5x)²-(4x)²=81
25x²-16x²=81
9x²=81
x²=9
x=√9
x=±3

4x=12,-12
5x=15,-15

Therefore, the numbers can be 12 and 15 OR -12 and -15.