"Question 16 What are the possible expressions for the dimensions of the cuboids whose volumes are given below?
Volume: 3x^2 - 12x Volume: 12ky^2 + 8ky - 20k
I II
Class 9 - Math - Polynomials Page 50"
Answers
Problem based on geometrical figure:
First we determine all the factors of the given polynomial by splitting middle term and then consider any of the factor as any of the dimension.
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Solution:
(i) Volume : 3x² – 12x
Since, volume is product of length, breadth and height therefore by factorizing the given volume, we can know the length, breadth and height of the cuboid.
3x²– 12x
= 3x(x – 4)
Hence,possible expression for length = 3
Possible expression for breadth = x
Possible expression for height = (x – 4)
(ii) Volume : 12ky² + 8ky – 20k
Since, volume is product of length, breadth and height therefore by factorizing the given volume, we can know the length, breadth and height of the cuboid.
12ky² + 8ky – 20k
= 4k(3y² + 2y – 5)
[By middle term splitting]
= 4k(3y² +5y-3y-5)
= 4k[y(3y+5)-1(3y+ 5)]
= 4k (3y +5) (y – 1)
Hence,possible expression for length = 4k
Possible expression for breadth = (3y +5)
Possible expression for height = (y – 1)
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