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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 \(35y^2 + 13y - 12\)
Answer :

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.