The dimensions of the cuboid are in the ratio 5 : 4 : 3 and its total surface area is 423 cm square . find its volume

The dimensions of the cube are 5x by 4x by 3x
SA = 2( 5x*4x) + 2(4x*3x) + 2(3x * 5x) = 40x² + 24x² + 30x² = 94x²  = 423 sq cm
x² = 423/94 = 9/2
x = 3*2^-1/2

Sides are thus 15*2^-1/2 , 12*2^-1/2 , 9*2^-1/2

Volume = 5x *4x * 3x  =60x³ = 60* (3*2^-1/2)³  = 60*27*2^-3/2 = 60*27/2*2^-1/2 810*2^-1/2 = 450*2^1/2 cm³