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The dimensions of a rectangular box …

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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 ₹8and ₹9.50 per metre square is ₹1248 find the dimensions of the box

Posted by Himanshu Gupta 4 years, 6 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 4 years, 6 months ago

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

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