Question

A rectangular park has length and breadth of 2 km and 1 km respectively. Due to the metro construction, the authority reduces the length and breadth of the park by $x$ km. Find the new area of the park in terms of $x$.

Answer 1

New length = $(2-x)km$
New breadth = $(1-x)km$

We know that, new area of the rectangular park:

= length $\times$ breadth
= $(2-x)(1-x)$
= $2(1-x)-x(1-x)$
= $2-2x-x+x^2$
= $2-3x+x^2$
= $(x^2-3x+2)k{m}^2$ (rearranging the terms)

Therefore, area of the park will be $(x^2-3x+2)k{m}^2$.