If the difference between the sides of a right angle triangle is 3 cm and its area is 54 CM square find its perimeter

Let the base be 'x' and the height be 'y'. So,

Area = 1/2(base x height) = 1/2(xy)=54       -----(1)

Now, x-y=3 => x=y+3      -----(2)

From (1) and (2),

1/2[(y+3)y]=54
y²+3y=108
solving the equation,we get,
y=9, -12

As side cannot have a negative value, y=9 is considered.
Now, x=y+3 so x=12.

Now, Hypotenuse = (x²+y²)^1/2
                              =(12²+9²)^1/2
                              =(225)^1/2
                              = 15 cm.
So, perimeter = x+y+hypotenuse = 12+9+15= 36cm.