Give possible expressions for the length and breadth of each of the following rectangles,in which their areas are given: $\text{Area} = 35y^2 + 13y - 12$.

(A) The area of a rectangle is given by the formula: $\text{Area} = \text{Length} \times \text{Breadth}$.
Given the area is $35y^2 + 13y - 12$,we need to factorise this quadratic polynomial.
To factorise $35y^2 + 13y - 12$,we split the middle term $13y$ into two parts such that their sum is $13y$ and their product is equal to the product of the coefficient of $y^2$ and the constant term $(35 \times -12 = -420)$.
We find that $28y$ and $-15y$ satisfy these conditions because $28y - 15y = 13y$ and $28y \times (-15y) = -420y^2$.
Now,rewrite the expression:
$35y^2 + 28y - 15y - 12$
Group the terms:
$(35y^2 + 28y) - (15y + 12)$
Factor out the common terms:
$7y(5y + 4) - 3(5y + 4)$
$(7y - 3)(5y + 4)$
Thus,the possible expressions for the length and breadth are $(7y - 3)$ and $(5y + 4)$.