Question

the total surface area of a cuboid is 63200cm square and its length,breadth and height are in the ratio 8:5:3 .Find the dimensions of the cuboid?

Answer 1

Length = 8x
breadtg = 5x
height  = 3x

TSA = 2(lb+bh+lh) = 63200
⇔2(8x*5x+5x*3x+8x*3x) = 63200
⇔2(40x²+15x²+24x²) = 63200
⇔2*79x² = 63200
⇔158x² = 63200
⇔x² = 63200/158= 400
⇔ x = 20 cm

Dimensions are:
Length = 20*8 =160cm
breadth = 20*5 = 100cm
height = 20*3 = 60cm 

Answer 2

ratio = 8 :  5 : 3 
l = 8x 
b = 5x 
h = 3x

total surface area = 2(lb+bh+hl)
=> 2 ( 8x*5x+5x*3x+3x*8x) = 63200
=> 2 (40x²+15x²+24x²) = 63200
=> 2*79x² = 63200
=> 158x² =  63200
=> x² = 63200/158 = 400
=> x = 20
 dimensions = 8x = 8*20 = 160 cm
 5x = 5*20 = 100 cm 
3x = 3*20 = 60 cm