Question

Area : 25a2 – 35a +12. Give possible expressions for the length And breadth of each of the following rectangle in which their areas,are given​

Answer 1

Given that the area of the rectangle is of the form 25a² -35a+12

To find:

The dimensions of the rectangle

•Factors of the equation would be the length and breadth of the rectangle

Factorizing,

25a²-35a+12=0

→25a²-20a-15a+12=0

→5a(5a-4)-3(5a-4)=0

→(5a-4)(5a-3)=0

→5a-4=0 or 5a-3=0

→a=4/5 or 3/5

The length and breadth could be 4/5 units and 3/5 units

Answer 2

$\bf{\large{\underline{\underline{Answer:-}}}}$

Length = (5a - 3) and breadth = (5a - 4)

$\bf{\large{\underline{\underline{Explanation:-}}}}$

Given : -Area of Rectangle = 25a² - 35a + 12

To find :- Length and breadth of the rectangle

Solution :-

Area of Rectangle = 25a² - 35a + 12

$\boxed{\sf{ \star\:\:Area\:of\:Rectangle = Length \times Breadth}}$

Area of the given rectangle = 25a² - 35a + 12

As area of rectangle is Product of two dimensions. And we are given an expression i.e, 25a² - 35a + 12. So, we need to factorize it to know the products.

Factorization of 25a² - 35a + 12

Length * Breadth = 25a² - 35a + 12

Split the middle terms :-

[25 * 12 = 300

300 = 2 * 2 * 5 * 5 * 3

300 = 20 * 15

So, - 35a = 20a - 15a]

= 25a² - 20a - 15a + 12

= 5a(5a - 4) - 3(5a - 3)

= (5a - 3)(5a - 4)

So, Length = (5a - 3) and breadth = (5a - 4)

For different values of we can get different lengths and breadths.

$\bf{\large{\underline{\underline{Extra\:Info-}}}}$

What is factorisation ?

Factorization is a process of writing the expression as a product of its factors.

1) Factorization by grouping the terms :-

Example :-

ax + bx + ay + by

= x(a + b) + y(a + b)

= (x + y)(a + b)

2) Factorization using identities :-

Example:- 25p² - 49q²

= (5p)² - (7q)²

= (5p + 7q)(5p - 7q) [Since a² - b² = (a + b)(a - b)