The sides of a right angled triangle are in A.P. If the triangle has area 24, then what is the length of its side?

Let x be the base, x+d be the hypotenuse and x-d be the other side.
Then, 1/2(x-d)(x) = 24
By Pythagoras theorem, (x-d)² + (x)² = (x+d)²
x² + x² + d² - 2xd = x² + d² + 2xd
x² = 4xd
x = 4d
Therefore, the sides of triangle become 3d, 4d, 5d
Now using the above equation
1/2(3d)(4d) = 24
6d² = 24
d² = 4
d = 2
The smallest side will be 3d = 3 × 2 = 6