Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given : $\boxed{\rm {Area}\,:35{y^2}+ 13y - 12}$
Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given : $\boxed{\rm {Area}\,:35{y^2}+ 13y - 12}$
Area of a rectangle $=$ (Length) $\times$ (Breadth)
Area $=$ $35 y^{2}+13 y-12$
We have to factorise the polynomial : $35 y^{2}+13 y-12$
Splitting the middle term we get
$13 y =28 y -15 y$ $ [\because 28 \times(-15)=-420$ and $-12 \times 35=-420]$
$\therefore 35 y ^{2}+13 y -12=35 y ^{2}+28 y -15 y -12=7 y (5 y +4)-3(5 y +4)$
$=(5 y+4)(7 y-3)$
Thus, the possible length and breadth are $(7y-3)$ and $(5 y+4)$.
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