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Question

# The dimensions of a reactangular box are in the ratio 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. 1,248. Find the dimensions of the box.

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Solution

## Ratio in the dimensions of a box = 2:3:4 Difference in total cost= Rs 1,248 Difference in rates = Rs. 9.50-rs.8 =Rs. 1.50 Let length (l) = 2x Then breadth (b) = 3x and height (h) = 4x \therefore Surface area = 2(l×b+b×h+h×l) = 2(2x×3x+3x×4x+4x×2x) = 2(6x2+12x2+8x2)=2×26x2=52x2 First rate of paper = Rs. 9.50 per m2 and second rate = 8.00 per m2 ∴ First cost = Rs. 52x2×9.50 and second cost = Rs 52x2× 8 ∴52x2×9.50−52x2× 8 ⇒52x2 (9.50-8)= 1248 ⇒52x2 (1.50) = 1248 ⇒x2=124852×1.50=1248×10052×150=16 ⇒x=√164 ∴ Length = 2x= 2× 4 = 8 m Breadth = 3x=3×4 = 12 m Height = 4x= 4×4 = 16 m

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