Question

If the height of a triangle is decreases by 40% and it's base is increased by40% what will be the percentage change in it's area​

Answer 1

Answer:

The % of change will be 16%.

Step-by-step explanation:

Let the initial height be h and initial base be b.

Then, area of Triangle initially = (1/2)*b*h

Now, new height = h - (40% of h) = h - 4h/10 = (10h - 4h)/10 = 6h/10 = 3h/5

New base = b + (40% of b) = b + 4b/10 = (10b+4b)/10 = 14b/10 = 7b/5

Thus, new area = (1/2)*(7b/5)*(3h/5) = (21/50)*b*h

Change in area = (1/2)*b*h - (21/50)*b*h = bh(1/2 - 21/50) = bh((25 - 21)/50) = 4/50 * bh = 2bh/25

Thus, % of change = [(Change in area * 100)/(Initial area)]% = (2bh*100/25)/(bh/2) = 8bh / (bh/2) = 8bh * 2/bh = 8*2 = 16%

Hence the % of change will be 16%.