the dimensions of a rectangular box are in a ratio 2:3:4 and the difference between the cost of coveringit with sheet of paper at the rate of rs.8 and rs.9.50 per m 2 is rs.1248. find the dimension of the box
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Let common multiple of 2:3:4 be x
=> Breadth = 2x
=> Length = 3x
=> Height = 4x
Surface area = 2(2x*3x + 3x*4x + 4x*2x) = 2(6x²+12x²+8x²) = 52x² cm²
As per question,
=> Rs. [9.5(52x²)-8(52x²)] = Rs. 1248
=> 1.5(52x²) = 1248
=> x² = 1248/(1.5*52) = 16
=> x = √16 = 4
∴ Breadth = 2(4) = 8cm
∴ Length = 3(4) = 12cm
∴ Height = 4(4) = 16cm
=> Breadth = 2x
=> Length = 3x
=> Height = 4x
Surface area = 2(2x*3x + 3x*4x + 4x*2x) = 2(6x²+12x²+8x²) = 52x² cm²
As per question,
=> Rs. [9.5(52x²)-8(52x²)] = Rs. 1248
=> 1.5(52x²) = 1248
=> x² = 1248/(1.5*52) = 16
=> x = √16 = 4
∴ Breadth = 2(4) = 8cm
∴ Length = 3(4) = 12cm
∴ Height = 4(4) = 16cm
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