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

Area of a rectangle $=$ (Length) $\times$ (Breadth)

Area $=25 a^{2}-35 a+12$

We have to factorise the polynomial: $25 a^{2}-35 a+12$

Splitting the co-efficient of $a$, we have

$-35 =(-20)+(-15)$       $[\because 25 \times 12=300$ and $(-20) \times(-15)=300] $

$25 a ^{2}-35 a +12 =25 a ^{2}-20 a -15 a +12$

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

Thus, the possible length and breadth are $(5 a-3)$ and $(5 a-4)$.