Question

Question 15
Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:
$\begin{array}{c}\begin{array}{c}Area:25a^2-35a+12\end{array}\\ \left(i\right)\end{array}\begin{array}{c}\begin{array}{c}Area:35y^2+13y-12\end{array}\\ \left(ii\right)\end{array}$

Answer 1

Here, area is given in terms of a quadratic expression in one varaible. To find the possible length and breadth of a rectangle, we have to factorise the given expression.

$\left(i\right)Area=25a^2-35a+12(Area=l\times b)=25a^2-20a-15a+12\left(splittingmiddleterm\right)=5a(5a-4)-3(5a-4)=(5a-4)(5a-3)$
So, possible answer is length = (5a-4), breadth = (5a-3) or vice versa.

$\left(ii\right)Area=35y^2+13y-12(Area=l\times b)=35y^2+28y-15y-12\left(splittingmiddleterm\right)=7y(5y+4)-3(5y+4)=(5y+4)(7y-3)$
So, (5y + 4) may be taken as breadth and (7y - 3) as length.