What are the possible expressions for the dimensions of the cuboids whose volumes are given below?
(i) Volume : 3x²–12x
(ii) Volume : 12ky²+8ky–20k
Answers
Answer:
Step-by-step explanation:
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.
---------------------------------------------------------------------------------------------------
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)
=========================================================
Hope this will help you...
Step-by-step explanation:
(i) Volume : 3x² - 12x
↪3x²- 12x can be written as 3x(x-4) by taking 3x out of both the terms.
●Possible expression for length = 3
●Possible expression for breadth = x
●Possible expression for height = (x-4)
___________________
(ii) Volume: 12ky²+8ky-20k
↪12ky²+8ky- 20k can be written as 4k(3y²+2y-5) by taking 4k out of both the terms.
↪12ky²+8ky-20k = 4k(3y²+2y-5)
[Here, 3y²+2y-5 can be written as 3y²+5y-3y-5 using splitting the middle term method.]
↪ 4k(3y²+5y-3y-5)
↪ 4k[y(3y+5)-1(3y+5)]
↪ 4k(3y+5)(y-1)
● Possible expression for length = 4k
●Possible expression for breadth = (3y +5)
●Possible expression for height = (y - 1)