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Total Surface Area of a Cuboid

What are the ...

Question

What are the possible expressions for the dimensions of the cuboid whose volume is $2 x^{2} + 10 x + 12$ ?

Length

= 2,

Breadth

= x + 3,

Height

= x + 2

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Length

= 5,

Breadth

= x + 4,

Height

= x + 3

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Length

= 3,

Breadth

= x + 6,

Height

= x + 2

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Length

= 4,

Breadth

= x - 12,

Height

= x - 1

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Solution

The correct option is A Length $= 2,$ Breadth $= x + 3,$ Height $= x + 2$
Volume of cuboid = ${2 x}^{2} + 10 x + 12 = 2 (x^{2} + 5 x + 6)$
= $2 (x^{2} + 3 x + 2 x + 6) = 2 (x + 3) (x + 2)$
$∴$ Length $= 2$ , breadth $= x + 3$ , height $= x + 2$

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What are the possible expressions for the dimensions of the cuboid whose volume is 2x2+10x+12?

The correct option is A Length =2, Breadth =x+3, Height =x+2Volume of cuboid = 2x2+10x+12=2(x2+5x+6) = 2(x2+3x+2x+6)=2(x+3)(x+2)∴ Length =2, breadth =x+3, height =x+2

What are the possible expressions for the dimensions of the cuboid whose volume is $2 x^{2} + 10 x + 12$ ?

The correct option is A Length $= 2,$ Breadth $= x + 3,$ Height $= x + 2$
Volume of cuboid = ${2 x}^{2} + 10 x + 12 = 2 (x^{2} + 5 x + 6)$
= $2 (x^{2} + 3 x + 2 x + 6) = 2 (x + 3) (x + 2)$
$∴$ Length $= 2$ , breadth $= x + 3$ , height $= x + 2$