Question

if the height of a triangle is decresed by 40% and its base is increased by 40% what will be the percentage change in its area

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Answer 1

Answer:

16

Step-by-step explanation:

Let height and base of the triangle be x and y units respectively

40% of x =2x/5

40% of y =2y/5

Now since  x  is decreased and  y  is increased, let

x′=x−2x/5=3x/5

y′=y+2y/5=7y/5

Therefore the new height is 3x/5 and the new base is 7y/5

Let  A=xy/2 and  A′={3x/5×7x/5}/2

Dividing  A  by  A′ , we get  25/21 . Let the areas be  25  unit sq  and  21 unit  sq

Percent change  =100(final−initial)/intial

Therefore percent change in area=100(21−25)/25

=16 %

Therefore area decreases by  16 %