Question

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Answer 1

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Answer 2

Given :

Sides of the cuboid are in the ratio 5 : 3 : 1

Let x be the common multiple, then we have

Length = 5x metres

Breadth = 3x metres

Height = x metres

Also, Total Surface area of cuboid = 414 sq.m

Surface area of cuboid=

$\tt{ {2(lb + bh + hl)}}$

$\tt \small{414 = 2(5x \times 3x + 3x \times x + 5x \times x})$

$\tt{414 = 2 \times (15x {}^{2} + 3x {}^{2} + 5 {x}^{2 }})$

$\tt{414 = 2 \times 23x {}^{2}}$

$\tt{ \frac{414}{2} = 23 \times x {}}^{2}$

$\tt{x {}^{2} = \frac{207}{23}}$

$\tt{ x {}^{2} = 9}$

$\tt{x = 3}$

Therefore,

Height = x = 3 metres

Breadth = 3x = 3 × 3 = 9 metres

Length = 5x = 5 × 3 = 15 metres

Final answer :

The dimensions are as follows

Length = 15 metres

Breadth = 9 metres

Height = 3 metres