Question

If the height of the triangle is decreased by 40 percent and its base is increased by 40 percent what will be the change in its area

Answer 1

Let height and base of the triangle be xx and yy units respectively.

4040% of x=2x5x=2x5

4040% of y=2y5y=2y5

Now since xx is decreased and yy is increased, let

x′=x−2x5x′=x−2x5

=3x5=3x5

y′=y+2y5y′=y+2y5

=7y5=7y5

Therefore the new height is 3x53x5 and the new base is 7y57y5.

Let A=xy2A=xy2 and A′=3x5×7x52A′=3x5×7x52

Dividing AA by A′A′, we get 25212521. Let the areas be 2525unitunit22 and 2121unitunit22.

Percent change =100(final−initial)intial=100(final−initial)intial

Therefore percent change in area

=100(21−25)25=100(21−25)25

−16%

Therefore area decreases by 16%.