Give possible expressions for the length and breadth of each of thefollowing rectangles, in which their areas are given: <br/> <br/>(i) Area: $25 \mathrm{a}^{2}-35 a+12$ <br/><br/>(ii) Area: $35 y^{2}+13 y-12$

Solution:

Area $=$ Length $\times$ Breadth

The expression given for the area of the rectangle has to be factorised. One of its factors will be its length and the other will be its breadth.

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

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

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

Therefore, possible length $=5 a-3$

And, possible breadth $=5 a-4$

(ii) $35 y^{2}+13 y-12=35 y^{2}+28 y-15 y-12$

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

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

Therefore, possible length $=5 y+4$

And, possible breadth $=7 y-3$