Q. 44.4( 24 Votes )

If each side of a triangle is doubled, then find percentage increase in its area.

Answer :

Given: Each side is doubled

To Find: Percentage change in the area.


Concept Used:


If sides of a triangle are a, b, and c, then area of a triangle is given by:



Where s = semiperimeter of the triangle



Assumption: Let the sides of the triangle be a, b, and c


Explanation:


Original Area,


As the sides are doubled, new sides are 2a, 2b, and 2c.



s’ = a + b + c


s’ = 2s






New Area = 4 times Original Area


Change in Area = New Area – Original Area


Change in Area = 3 times Original Area




%age change in area = 300 %


Hence, the percentage change in area is 300%.


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