Question

the dimensions of a cuboid are in ratio 4:3:2 and its total surface area is 208 cm square.Find its dimensions

Answer 1

let dimensions of cuboid are
length = l=4x cm
width = w =3x cm
height = h = 2x ( since given ratio 4:3:2)

total surface area = 208 cm
2(lw+wh+hl) = 208
2[4x*3x+3x*2x+2x*4x] =208

2[12x²+6x²+8x²]=208

2*26x²=208
52x²=208

x²=208/52
x²=4
x=2
therfore
l=4x=4*2 =8cm
w=3x=3*2=6cm
h=2x=2*2=4cm

Answer 2

Let dimensions of cuboid are length=l=4xcm, breadth=b=3xcm, height=h=2xcm(since given ratio 4: 3: 2) . TSA of cuboid= 208 cm sq. 2(lb+lh+bh)=208cm 2(4x