Question

the length breadth and hight of cuboid are in the ratio 5: 4: 2. if the total surface area is 1216cm, find the dimensions of the cuboid​

Answer 1

Given:

• The length breadth and hight of cuboid are in the ratio = 5: 4: 2.
• The total surface area is = 1216 cm.

To find :

• The dimensions of the cuboid =?

Step-by-step explanation :

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

As We know that,

★The total surface area of the cuboid = 2 ( LB + BH + HL ).

Substituting the values in the above formula,

we get,

==> 2( LB + BH + HL ) = 1216

==> 2(5x × 4x + 4x × 2x + 2x × 5x) = 1216

==>2(20x² + 8x² + 10x²) = 1216

==>2× 38x² = 1216

==>76x²= 1216

==> x² = 1216/76

==>x² = 16

==> x = 4

So,Now calculate dimensions of cuboid .

• first dimension = 5x = 5 × 4 = 20 cm
• second dimension = 4x = 4×4 = 16 cm
• third dimension = 2x = 2×4 = 8 cm

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Some Other Formula

★ Volume of cuboid = l × w × h

★space diagonal of cuboid = √(l² + w² + h²)

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Answer 2

Answer:

• The dimensions of cuboid are 20 cm,16 cm and 08 cm.

Solution:-

Given:-

• Length,breadth and height of cuboid are in the ratio 5:4:2.
• The total surface area of cuboid is 1216 cm.

To Find:

• The dimension of the cuboid.

Formula Required:-

• Total surface area(TSA) of cuboid = 2(l×b + b×h + h×l)

Step-by-step explanation:

• Let the dimensions be 5x : 4x : 2x respectively.

Then,

$\\ :\implies\sf{1216=2(5x\;\times\;4x\; + \;4x\;\times\;2x\;+\;2x\;\times\;5x)}\\ \\ :\implies\sf{1216=2(20x^2+8x^2+10x^2)}\\ \\ :\implies\sf{1216=2\times38x^2}\\ \\ :\implies\sf{\frac{\cancel{1216}}{\cancel{2}}=38x^2}\\ \\ :\implies\sf{608=38x^2}\\ \\ :\implies\sf{x^2=\frac{\cancel{608}}{\cancel{38}}}\\ \\ :\implies\sf{x=\sqrt{16}}\\ \\ :\implies\underline{\boxed{\mathfrak{x=4}}}\;\bigstar$

Therefore,

• Length = 5x = 5(4) = 20 cm
• Breadth = 4x = 4(4) = 16 cm
• Height = 2x = 2(4) = 8 cm

Hence,

• The dimensions of the cuboid are 20 cm,16 cm and 8 cm.