Question

A square that is 2009 by 2009units has its length decreased by 50 and its width increased by 50. By how many square units does its area change?

Answer 1

area of the original square=2009*2009=4036081 sq.units

area of the changed square=(2009+50)*(2009-50)

=2059*1959=4033581 sq.units

hence the area changes by (4036081-4033581)sq.units

the area changes by 3500 sq.units

Answer 2

Let 2009 = a for easy calculation

Present area of rectangle = a*a = a² sq units

New area = (a-50% of a) * (a + 50% of a)

= a-a/2 * a+a/2

= a/2 * 3a/2

= 3/2 a² sq units

Area Change = New Area - Old Area

= 3/2a² - a²

= a²/2