Question

Give possible expressions for the length and breadth of the rectangle whose area is given by
(i) $25a^2-35a+12$
(ii) $24x^2-15x$

Answer 1

(i) Let us first factorize the given expression $25a^2-35a+12$ as shown below:

$25a^2-35a+12=25a^2-15a-20a+12=5a(5a-3)-4(5a-3)=(5a-4)(5a-3)$

Therefore, the area of the rectangle is $(5a-4)(5a-3)$ and we also know that the area of the rectangle is $A=$length$\times$breadth.

Hence, the length and breadth can both be $(5a-4)$ or $(5a-3)$.

(ii) Let us first factorize the given expression $24x^2-15x$ as shown below:

$24x^2-15x=x(24x-15)$

Therefore, the area of the rectangle is $x(24x-15)$ and we also know that the area of the rectangle is $A=$length$\times$breadth.

Hence, the length and breadth can both be $x$ or $(24x-15)$.