Give possible expressions for the length and breadth of each of the following rectangles,in which their areas are given: $\text{Area} = 25a^2 - 35a + 12$

(A) The area of a rectangle is given by the formula: $\text{Area} = \text{Length} \times \text{Breadth}$.
Given the area: $25a^2 - 35a + 12$.
To find the length and breadth,we need to factorise the quadratic polynomial $25a^2 - 35a + 12$ by splitting the middle term.
We look for two numbers whose product is $25 \times 12 = 300$ and whose sum is $-35$.
These two numbers are $-20$ and $-15$,since $(-20) \times (-15) = 300$ and $(-20) + (-15) = -35$.
Now,rewrite the expression:
$25a^2 - 20a - 15a + 12$
Factor by grouping:
$= 5a(5a - 4) - 3(5a - 4)$
$= (5a - 4)(5a - 3)$
Thus,the possible expressions for the length and breadth are $(5a - 3)$ and $(5a - 4)$.