Question

the length, breadth and height of a cuboid are in the ratio 5:4:2 and its total sur face area is 1216 cm2. Find the dimensions of the cuboid.

Answer 1

Answer :

Length = 20 cm

Breadth = 16 cm

Height = 6 cm

Step-by-step explanation:

Let the length, breadth and height of a cuboid be 5x , 4x and 2x respectively.

According to the question ;

Total Surface Area of cuboid = 1216 cm²

⇒ 2 ( lb + bh + hl ) = 1216

⇒ 2 ( 5x * 4x + 4x * 2x + 2x * 5x ) = 1216

⇒ 2 ( 20x² + 8x² + 10x² ) = 1216

⇒ 38 x²  = 1216 / 2

⇒ 38 x² = 608

⇒ x² = 608 / 38

⇒ x² = 16

⇒ x = √16

⇒ x = 4 cm

Therefore, the dimensions of cuboid are ;

Length = 5x = 5 * 4 = 20 cm.

Breadth = 4x = 4 * 4 = 16 cm.

Height = 2x = 2 * 3 = 6 cm.

Answer 2

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Suppose the length, breadth and height of a cuboid is 5p , 4p and 2p

By the Information

TSA of cuboid = 1216 cm²

2 ( lb + bh + hl ) = 1216

2 ( 5p × 4p + 4p × 2p + 2p × 5p ) = 1216

2 ( 20p² + 8p² + 10p² ) = 1216

38 p²  = 1216 ÷ 2

38 p² = 608

p² = 608 ÷ 38

p² = 16

$\bf\huge p = \sqrt{16}$

p = 4 cm

Dimensions of cuboid are :

Length = 5p

= 5 × 4  

= 20 cm.

Breadth = 4p

= 4 × 4

= 16 cm.

Height = 2p

= 2 × 3

= 6 cm

Length = 20cm  

Breadth = 16cm , Height = 6cm

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