The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and

1.	The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost of covering it with sheet of paper at the rates of Rs. 8 and Rs. 9.50 per m2 is Rs. 1248. Find the dimensions of the box.
Answer» Given, Ratio of dimensions of rectangular box = 2:3:4 Let dimensions are = 2x ,3x , 4x So, total surface area of box = 2(6x²+12x²+8x²) = 52 x² Let, c₁ = cost of covering at rate Rs. 8 per m² C₁ = 8 × 52 x² Let c₂ = cost of covering at rate Rs.9.50 per m² C₂ = 9.50 × 52 x² = C₂ – C₁ = 1248(given) = 52x² × 9.50 – 52x²× 8 = 1248 = 52x² =\(\cfrac{1248}{1.50}\) = x² = \(\cfrac{1248}{1.50\times52}\)= 16 x = 4 Hence dimensions of box are = 2x = 2 × 4 = 8 cm = 3x = 3 × 4 = 12 cm = 4x = 4 × 4 = 16cm

The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost of covering it with sheet of paper at the rates of Rs. 8 and Rs. 9.50 per m2 is Rs. 1248. Find the dimensions of the box.

Answer»

Given,

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

Let dimensions are = 2x ,3x , 4x

So, total surface area of box = 2(6x²+12x²+8x²) = 52 x²

Let, c₁ = cost of covering at rate Rs. 8 per m²

C₁ = 8 × 52 x²

Let c₂ = cost of covering at rate Rs.9.50 per m²

C₂ = 9.50 × 52 x²

= C₂ – C₁ = 1248(given)

= 52x² × 9.50 – 52x²× 8 = 1248

= 52x² =\(\cfrac{1248}{1.50}\)

= x² = \(\cfrac{1248}{1.50\times52}\)= 16

x = 4

Hence dimensions of box are = 2x = 2 × 4 = 8 cm

= 3x = 3 × 4 = 12 cm

= 4x = 4 × 4 = 16cm