Question

The dimensions of a cuboid are in the ratio 2:3:4.its total surface area is 1872 cm2 .find its dimensions

Answer 1

Hope this help you..

Answer 2

The dimensions of cuboid are 12 cm and 18 cm and 24 cm

Solution:

Given that,

The dimensions of a cuboid are in the ratio 2 : 3 : 4

Let the length be 2x

Let the width be 3x

Let the height be 4x

The total surface area of cuboid is:

$TSA = 2(lw + lh + hw)$

Total surface area is 1872 cm^2

Therefore,

$1872 = 2( 2x \times 3x + 2x \times 4x + 4x \times 3x)\\\\1872 = 2(6x^2 + 8x^2 + 12x^2)\\\\26x^2 = 936\\\\x^2 = 36\\\\ x = 6$

Thus the dimensions are:

length = 2x = 2(6) = 12

width = 3x = 3(6) = 18

height = 4x = 4(6) = 24

Thus the dimensions of cuboid are 12 cm and 18 cm and 24 cm

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