Question

the surface area of a cuboid is 1372 CM square if its dimension are in the ratio 4 : 2 : 1, find its length

Answer 1

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The surface area of cuboid = 2 ( LB + BH + HL )

1372 cm = 2 ( LB + BH + HL )

Let the ratios be x. Then 4x, 2x & 1x

Let the length be = 4x

Breadth = 2x

Height = 1x

$= > 2(4x \times 2x + 2x \times 1x + 4x \times 1x) = 1372 \\ \\ = > 2(8 {x}^{2} + 2 {x}^{2} + 4 {x}^{2} ) = 1372 \\ \\ = > 2 \times 14 {x}^{2} = 1372 \\ \\ = > 28 {x}^{2} = 1372 \\ \\ = > {x}^{2} = \frac{1372}{28} \\ \\ = > {x}^{2} = 49 \\ \\ = > x = \sqrt{49} \\ \\ = > x = 7$

Length = 7 × 4 = 28
Breadth = 7 × 2 = 14
Height = 7 × 1 = 7

So these are the following dimensions of the cuboid
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Answer 2

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