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?
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?
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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
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