Question

10. 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 ?​

Answer 1

Answer:

Step-by-step explanation:

Let the original base and height of the triangle be b and h respectively.

Original Area - 1/2 * b * h = bh/2

Now, new base = 14/10 * b = 7b/5

and new height  = 14/10 * h = 7h/5

Therefore, New area = 1/2 * 7b/5 * 7h/5 = 49bh/50

Difference = new area - original area = 49bh/50 - bh/2 = 24bh/50

% change = 24bh/5 * 2/bh * 100 = 240%

Answer 2

Answer: Decrease in 16%

Let height be x units

Let base be y units

A = xy/2 sq. units

Decrease height by 40% = (40/100)*x = 2x/5

Increase base by 40% = (40/100)*y = 2y/5

So the decreased height is x - (2x/5) = 3x/5 units

and the increased base is y+ (2y/5) = 7y/5 units

A' = 21xy/25                  (since A = {1/2*}b*h)

On dividing A and A', we get

A/A' = 25/21

Therefore the areas are 25 sq. units and 21 sq. units

% change = [100 * {final - initial}] ÷ initial

=> 100(25-21) ÷ 25

=> 16%  

Therefore the area is decreased by 16%

Hope it helps.....