Question

Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given :
(i) Area : $25a^2-35a+12$ (ii) Area : $35y^2+13y-12$

Answer 1

$\left(i\right)$ $Area=25a^2-35a+12$

$\Rightarrow$ $25a^2-15a-20a+12$

$\Rightarrow$ $5a(5a-3)-4(5a-3)$

$\Rightarrow$ $(5a-3)(5a-4)$

Hence, $Area=(5a-3)(5a-4)$

We know, $Area=Length\times breadth$

Hence, there are two possibilities

$Case1:Length=(5a-3)$ and $Breadth=(5a-4)$

$Case2:Length=(5a-4)$ and $Breadth=(5a-3)$

$\left(ii\right)$ $Area=35y^2+13y-12$

$\Rightarrow$ $35y^2+28y-15y-12$

$\Rightarrow$ $7y(5y+4)-3(5y+4)$

$\Rightarrow$ $(5y+4)(7y-3)$

Hence, $Area=(5y+4)(7y-3)$

We know, $Area=Length\times breadth$

Hence, there are two possibilities

$Case1:Length=(5y+4)$ and $Breadth=(7y-3)$

$Case2:Length=(7y-3)$ and $Breadth=(5y+4)$