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The volume of a cuboid is 3x2 - 27, its possible dimensions are
- a)3, x2, -27x
- b)3, x - 3, x + 3
- c)3, x2, 27n
- d)3, 3, 3
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The volume of a cuboid is 3x2 - 27, its possible dimensions area)3, x2...
To find the possible dimensions of the cuboid, we need to factorize the given volume expression, 3x^2 - 27.
Factorizing the Volume Expression:
We can factorize the given expression by taking out the common factor, 3, from both terms:
3x^2 - 27 = 3(x^2 - 9)
Next, we notice that the expression in the brackets is a difference of squares, which can be further factorized:
x^2 - 9 = (x - 3)(x + 3)
Therefore, the volume expression can be completely factorized as:
3x^2 - 27 = 3(x - 3)(x + 3)
Identifying the Possible Dimensions:
The dimensions of a cuboid are represented by the length, width, and height. From the factorized volume expression, we can identify the dimensions as follows:
Length: x - 3
Width: x + 3
Height: 3
Checking the Options:
Now, let's check which option matches the possible dimensions we obtained:
a) 3, x^2, -27x
This option does not match the possible dimensions we obtained. The width should be (x + 3), not x^2, and the length should be (x - 3), not -27x.
b) 3, x - 3, x + 3
This option matches the possible dimensions we obtained. The width is (x + 3), the length is (x - 3), and the height is 3.
c) 3, x^2, 27n
This option does not match the possible dimensions we obtained. The width should be (x + 3), not x^2, and the length should be (x - 3), not 27n.
d) 3, 3, 3
This option does not match the possible dimensions we obtained. The width should be (x + 3), and the length should be (x - 3), not 3.
Therefore, the correct answer is option 'B': 3, x - 3, x + 3.
Factorizing the Volume Expression:
We can factorize the given expression by taking out the common factor, 3, from both terms:
3x^2 - 27 = 3(x^2 - 9)
Next, we notice that the expression in the brackets is a difference of squares, which can be further factorized:
x^2 - 9 = (x - 3)(x + 3)
Therefore, the volume expression can be completely factorized as:
3x^2 - 27 = 3(x - 3)(x + 3)
Identifying the Possible Dimensions:
The dimensions of a cuboid are represented by the length, width, and height. From the factorized volume expression, we can identify the dimensions as follows:
Length: x - 3
Width: x + 3
Height: 3
Checking the Options:
Now, let's check which option matches the possible dimensions we obtained:
a) 3, x^2, -27x
This option does not match the possible dimensions we obtained. The width should be (x + 3), not x^2, and the length should be (x - 3), not -27x.
b) 3, x - 3, x + 3
This option matches the possible dimensions we obtained. The width is (x + 3), the length is (x - 3), and the height is 3.
c) 3, x^2, 27n
This option does not match the possible dimensions we obtained. The width should be (x + 3), not x^2, and the length should be (x - 3), not 27n.
d) 3, 3, 3
This option does not match the possible dimensions we obtained. The width should be (x + 3), and the length should be (x - 3), not 3.
Therefore, the correct answer is option 'B': 3, x - 3, x + 3.
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Community Answer
The volume of a cuboid is 3x2 - 27, its possible dimensions area)3, x2...
Here 3x2 - 27 = 3(x2 - 9)
= 3[(x)2 - (3)2]
= 3(x + 3) (x - 3)
= 3[(x)2 - (3)2]
= 3(x + 3) (x - 3)
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