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

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

ii)Area \(35y^2 + 13y - 12\)

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

ii)Area \(35y^2 + 13y - 12\)

i)We have area of rectangle \(= 25a^2 - 35a + 12\)

\(= 25a^2 - 20a - 15a + 12\)

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

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

One possible answers : Length = 5a - 3, Breadth = 5a - 4.

ii)We have area of rectangle \(= 35y^2 + 13y - 12\)

\(= 35y^2 - 15y + 28y - 12\)

\(= 5y(7y - 3) + 4(7y - 3)\)

\(= (7y - 3)(5y + 4)\)

One possible answers : Length = 7y - 3, Breadth = 5y + 4.