the length of rectangular field is increased by 50% and its breadth is decreased by 50% to form a new rectangular field find the percentage change in the area of the field
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Let the length of rectangle be a
And width of rectangle be b
Area = ab
Now,
New length = a + 50% of a
= a+ 50a/100
= a+a/2
= 3a/2
New width = b - 50% of b
= b - b/2
= b/2
New Area = 3a/2 * b/2
= 3ab/4
Decrease in Area = ab - 3ab/4
= ab/4
% of Decrease in Area = [(ab/4) * 100] / ab
= 100 / 4
= 25 %
And width of rectangle be b
Area = ab
Now,
New length = a + 50% of a
= a+ 50a/100
= a+a/2
= 3a/2
New width = b - 50% of b
= b - b/2
= b/2
New Area = 3a/2 * b/2
= 3ab/4
Decrease in Area = ab - 3ab/4
= ab/4
% of Decrease in Area = [(ab/4) * 100] / ab
= 100 / 4
= 25 %
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