# The dimensions of

Ratio of dimensions of rectangular box = 2:3:4

Let length of box = 2x m

Breadth of box = 3x m

Height of box = 4x m

Area of sheet of paper required for covering it = total surface area of cuboid

= 2(lb × bh × hl)

=2(6x2 + 12x2 + 8x2)

= 2×26x2

=52 x2 m2

Cost of covering it with sheet of paper at Rs.9.50 /m2

= 52 x2 × 9.50

=Rs.494 x2

Cost of covering it with sheet of paper at rate Rs.8/m2 = 52x2 × 8

=Rs.416 x2

= 494x2-416x2=1248 Given

= 78x2=1248

= x2=1248/78=16

= x= √16=4

So,

Length of box = 2x = 2×4 = 8 m

Breadth of box = 3x = 3×4 = 12 m

Height of box = 4x = 4×4 = 16 m

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