what are the possible expression for the dimension of the cuboid whose volume is 12 m y square + 8 m y - 20 m
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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Hope this will help you...