Let's call the smallest side "x"

Therefore we have:x^2 + (x + 5)^2 = ( (x + 5) + 3)^2

Or in other words:x^2 + (x + 5)^2 = (x + 8)^2

Therefore:x^2 + x^2 + 10x + 25 = x^2 + 16x + 64

Subtract both sides by x^2 to get:x^2 + 10x + 25 = 16x + 64

Take 25 from both sides:x^2 + 10x = 16x + 39

Put it all on one side:x^2 - 6x - 39 = 0

Quadratic equation:x = [ -b +/- SQRT( b^2 - 4ac ) ] / ( 2a )

Substitute:x = [ -(-6) +/- SQRT( [-6]^2 - 4[1][-39] ) ] / ( 2[1] )

Which eventually becomesx ~ 9.92820323andx ~ -3.92820323

x can't be negative, so:x = 9.92820323 = 3 + 4[ SQRT(3) ]

So one side is3 + 4[ SQRT(3) ]

The other is8 + 4[ SQRT(3) ]

And the hypotenuse is:11 + 4[ SQRT(3) ]