Question

The dimension of a cuboid are in the ratio 3: 4: 5 and its total surface area is 188 m2. Find the dimension of cuboid in (m).

Answer 1

Given:-

• Dimension of a cuboid = 3 : 4 : 5

• It's Total Surface Area = 188 m²

To Find:-

• Dimension of cuboid in (m).

Formula used:-

• ${\boxed{TSA\:of\:Cuboid=2(lb + bh + hl)}}$

Solution:-

Let the Length, Breadth and Height of the cuboid be 3x, 4x, and 5x respectively.

Now, Using Formula

$:\implies\:TSA\:of\:Cuboid=2(lb + bh + hl)$

$:\implies\:188=2(3x\times4x + 4x\times5x + 5x\times3x)$

$:\implies\:188=2(12x^2 + 20x^2 + 15x^2)$

$:\implies\:94=47x^2$

$:\implies\:x^2=\dfrac{94}{47}$

$:\implies\:x^2=2$

${\boxed{:\implies\:x=\sqrt{2}}}$

Hence,

• Length = 3x = 3 × √2 = 3√2m

• Breadth = 4x = 4 × √2 = 4√2m

• Height = 5x = 5 × √2 = 5√2m

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Answer 2

Answer:

Let the length of the cuboid = x, breadth = 2x, height = 3x

Total surface ares of a cuboid = 2(l+b+b×h+l×h)

Given, total surface area of the cuboid = 88m^2

Step-by-step explanation:

= 2(x × 2x + 2x × 3x + x × 3x) = 88m^2

= 22x^2 = 88

= x = 2

Hence, the length of the cuboid = x=2m, breadth = 2x = 4m, height = 3x = 6m