Question

The length, breadth and height of a cuboid are in the ratio 5:4:3.
The total surface area is 846 cm square.
Find the length, breadth and height of the cuboid. *​

Answer 1

Given :

⬤ Length , Breadth and Height of a Cuboid are in the Ratio 5:4:3 .

⬤ Total Surface Area of Cuboid is 846 cm² .

To Find :

⬤ Length , Breadth and Height of Cuboid .

Formula Used :

$\bf[\:{Total\:Surface\:Area\:of\:Cuboid=2(lb+bh+hl)}\:]$

• l = Length
• b = Breadth
• h = Height

Solution :

Let :

• Length of Cuboid be 5x .
• Breadth of Cuboid be 4x .
• Height of Cuboid be 3x .

According to the Formula :-

846 = 2(5x*4x + 4x*3x + 3x*5x)

846/2 = 20x² + 12x² + 15x²

423 = 47x²

423/47 = x²

9 = x²

√9 = x

3 = x

Therefore , The Value of x is 3 .

Hence ,

Length of Cuboid = 5x

= 5(3)

= 15

Breadth of Cuboid = 4x

= 4(3)

= 12

Height of Cuboid = 3x

= 3(3)

= 9

Therefore , Length , Breadth and Height of Cuboid are 15 cm , 12 cm and 9 cm .

Answer 2

$\huge\underline{\bf \orange{AnSweR :}}$

• 846 = 2(5x*4x + 4x*3x + 3x*5x)

• 846/2 = 20x² + 12x² + 15x²

• 423 = 47x²

• 423/47 = x²

• 9 = x²

• √9 = x

• 3 = x

Therefore , The Value of x is 3 .

Hence ,

Length of Cuboid = 5x

= 5(3) = 15

Breadth of Cuboid = 4x

= 4(3) = 12

Height of Cuboid = 3x

= 3(3) = 9

Therefore , Length , Breadth and Height of Cuboid are 15 cm , 12 cm and 9 cm .