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Mathematics

The dimensions of a rectangular box are in the ratio 4 : 2 : 3. The difference between cost of covering it with paper at 12 per m2 and with paper at the rate of 13.50 per m2 is ₹ 1,248. Find the dimensions of the box.

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Answer

Given:

The ratio of dimensions of the rectangular box = 4 : 2 : 3

Let the dimension be 4a, 2a and 3a.

Total surface area of box = 2(lb + bh + hl)

= 2(4a x 2a + 2a x 3a + 3a x 4a)

= 2(8a2 + 6a2 + 12a2)

= 2 x 26a2

= 52a2

The difference between cost of covering it with paper at 12 per m2 and with paper at the rate of 13.50 per m2 = ₹ 1,248

⇒ Total surface area x 13.5 per m2 - Total surface area x 12 per m2 = ₹ 1,248

⇒ 52a2 x 13.5 - 52a2 x 12 = ₹ 1,248

⇒ 52a2 (13.5 - 12) = ₹ 1,248

⇒ 52a2 x 1.5 = ₹ 1,248

⇒ 78a2 = ₹ 1,248

⇒ a2 = 1,24878\dfrac{1,248}{78}

⇒ a2 = 16

⇒ a = 16\sqrt{16}

⇒ a = 4 m

So, the dimensions are 4a, 2a and 3a

= 4 x 4 m, 2 x 4 m and 3 x 4 m

= 16 m, 8 m and 12 m

Hence, the dimensions of the box are 16 m , 8 m and 12 m.

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