Polynomials

Exercise 2.5 Part 12

Question 15: Give possible expression for the length and breadth of each of the following rectangles, in which their areas are given:

(i) Area `= 25a^2 - 35a + 12`

Answer: Given, `25a^2 - 35a + 12`

By splitting the middle term, we get:

`25a^2 - 15a – 20a + 12`

`= 5a(5a – 3) – 4(5a – 3)`

`= (5a – 3)(5a – 4)`

Hence, possible length `= 5a – 3`
Possible breadth `= 5a – 4`


(ii) Area `= 35y^2 + 13y – 12`

Answer: Given, `35y^2 + 13y – 12`

By splitting the middle term, we get:

`= 35y^2 + 28y – 15y – 12`

`= 7y(5y + 4) – 3(5y + 4)`

`= (5y + 4)(7y – 3)`

Hence, possible length `= 5y + 4`
Possible breadth `= 7y – 3`


Question 16: What are the possible expressions for the dimensions of the cuboids whose volumes are given below?

(i) Volume: `3x^2 - 12x`

Answer: Given; `3x^2 - 12x`

`= 3x(x – 4)`

We know that, volume = length x breadth x height

Hence, possible length = 3
Possible breadth `= x`
Possible height `= (x – 4)`

(ii) Volume: `12ky^2 + 8ky – 20k`

Answer: Given: `12ky^2 + 8ky – 20k`

By taking 4k as common, we get:

`= 4k(3y^2 + 2y – 5)`

By splitting the middle term, we get:
`4k(3y^2 - 3y + 5y – 5)`

`= 4k[3y(y – 1) + 5(y – 1)]`

`= 4k((y – 1)(3y + 5)`

We know that volume = length x breadth x height

Hence, possible length `= 4k`
Possible breadth `= (y – 1)`
Possible height `= (3y + 5)`



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