Question

The dimensions of a cubiod are in ratio 2:3:4 and its Total surface area is 468m² . Find the dimensions.​

Answer 1

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Answer 2

Answer:

Dimensions → 6 m, 9 m and 12 m

Step-by-step explanation:

Let  the dimensions of the cuboid be:

• Length = l = 2x
• Breadth = b = 3x
• Height = h = 4x

We know that:

   TSA of cuboid = 2 (lb + bh + hl)

⇒ 468 = 2 [(2x)(3x) + (3x)(4x) + (4x)(2x)]

⇒ 468 = 2 [6x² + 12x² + 8x²]

⇒ 468 = 2 (26x²)

⇒ 468 = 52 x²

⇒ x² = 468 ÷ 52

⇒ x² = 9

⇒ x = √9 = ± 3

Side cannot be negative.

So, x = 3.

Now, let's find out Length, Breadth and Height.

• Length = 2x = 2(3) = 6 m
• Breadth = 3x = 3(3) = 9 m
• Height = 4x = 4(3) = 12 m

∴ The dimensions of cuboid are 6 m, 9 m and 12 m.