Question

if the height of ttiangle is increased by 40% and base is increased by 40%. what will be percentage change in the area

Answer 1

Answer:

If the height of a triangle is decreased by 40%, and its base is increased by 40%, what will be the percentage change in its area?

Let the base and height of original triangle be b units and h units respectively. Then the area of the triangle is 1/2 bh sq units.

When the base b is increased by 40% it becomes 140b/100.

When the height is decreased by 40% it becomes 60h/100.

The new area of the triangle is

(1/2)(140b/100)(60h/100) = (84/100)(1/2bh).

The area of the triangle decreases by 16%

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

40% of x=2x5

40% of y=2y5

Now since x is decreased and y is increased, let

x′=x−2x5

=3x5

y′=y+2y5

=7y5

Therefore the new height is 3x5 and the new base is 7y5.

Let A=xy2 and A′=3x5×7x52

Dividing A by A′, we get 2521. Let the areas be 25unit2 and 21unit2.

Percent change =100(final−initial)intial

Therefore percent change in area

=100(21−25)25

−16%

Therefore area decreases by 16%.

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