Question

The dimensions of a cuboid are in the ratio 1: 2: 3 and its total surface area is 88 m2. find the dimensions.

Answer 1

Hi friend ✋✋✋✋
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Your answer
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Ratio between the dimensions of a cuboid = 1:2:3

Total surface area of the cuboid = 88 m²

Let the dimensions of the cuboid be x , 2x and 3x respectively .

Then,
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2 × [(x × 2x) + (x × 3x) + (2x × 3x)] = 88

=> 2x² + 3x² + 6x² = 88/2

=> 11x² = 44

=> x² = 44/11

=> x² = 4

=> x = √4

=> x = 2 m

Then,
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Height = x = 2m

Breadth = 2x = ( 2 × 2) m = 4m

Length = 3x = (3 × 2) m = 6m

HOPE IT HELPS

Answer 2

AnswEr:

Dimensions of the cuboid are in the ratio

• 1 : 2 : 3

So, let the dimensions be

• x, 2x, 3x in metres.

__________________________

Now,

◕$\qquad\tt{Surface\:area=88m^2}$

$\Rightarrow$ $\tt{2(x\times\:2x+2x\times\:3x+x\times\:3x)=88}$

$\Rightarrow$ $\tt{2(2x^2+6x^2+3x^2)=88}$

$\Rightarrow$ $\tt{2\times\:11x^2=88}$

$\Rightarrow$ $\tt{22x^2=88}$

$\Rightarrow$ $\tt{x^2=}$$\tt\dfrac{88}{22}$

$\Rightarrow$ $\tt{x^2=4}$

$\Rightarrow$ $\tt{x^2=2^2}$

$\Rightarow$ $\tt{x=2m}$

$\therefore$ $\sf{2x=2\times\:2=4\:and\:3x=3\times\:2=6}$

$\underline\mathfrak{Hence,\:dimensions\:are\:2m,\:4m\:and\:6m}$

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