Question

Given the area of rectangle is A $=25a^2-35a+12$. The length is given as ($5a-3$). Therefore, the width is?

Answer 1

To find the width of the rectangle, we divide the area of the rectangle with its length.

$\therefore$ Breadth $=\frac{25a^2-35a+12}{(5a-3)}$

Consider, $25a^2-35a+12$

Using Middle Term Splitting, to factories the given expression,

Here the product of required numbers is $25a^2\times 12=300$ and the required sum is $-35a$

Therefore, the numbers are $-15a$ and $-20a$

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

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

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

$\therefore 25a^2-35a+12=(5a-3)(5a-4)$

Hence, Breadth $=\frac{25a^2-35a+12}{(5a-3)}=\frac{(5a-3)(5a-4)}{(5a-3)}=(5a-4)$