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 $x$.

• A. $-x^2+3x+2$
• B. $x^2-3x-2$
• C. $x^2+3x+2$
• D. $x^2-3x+2$

Answer 1

The correct option is D $x^2-3x+2$


So, new length = $(2-x)km$
and new breadth = $(1-x)km$

We know that, new area of the rectangular park (portion in blue color)

= length $\times$ breadth
= $(2-x)(1-x)$
= $2(1-x)-x(1-x)$
= $2-2x-x+x^2$
= $2-3x+x^2$ (grouping the like terms)
= $(x^2-3x+2)k{m}^2$ (rearranging the terms)
Therefore, area of the park will be $(x^2-3x+2)k{m}^2$.