Let A = value of perpendicular

Let B = value of leg facing side 9

Let C = value of leg facing side 16

We can write the following equations

9^2 + A^2 = B^2

16^2 + A^2 = C^2

B^2 + C^2 = 25^2

Then,

2A^2 + 9^2 + 16^2 = 25^2 , A = 12

9^2 + 12^2 = B^2 , B = 15

16^2 + 12^2 = C^2 C = 20