Q. 124.7( 6 Votes )

# The dimensions of

Answer :

Let

Length of cuboid = l = 5x

Breadth of cuboid = b = 3x

Height of cuboid = h = 2x

Such that the ratio is 5:3:2 as mentioned in question where x is any positive number

Total surface area of cuboid = 558 cm^{2}

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

⇒ 558 = 2 × [(5x)(3x) + (3x)(2x) + (2x)(5x)]

⇒ = 15x^{2} + 6x^{2} + 10x^{2}

⇒ 279 = 31x^{2}

⇒ x^{2} =

⇒ x^{2} = 9

⇒ x = ± 3

x is length therefore x cannot be negative therefore x = 3

therefore,

length of cuboid = 5x = 5 × 3 = 15 cm

breadth of cuboid = 3x = 3 × 3 = 9 cm

height of cuboid = 2x = 2 × 3 = 6 cm

length of edges of cuboid are 15 cm, 9 cm and 6 cm

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