Question

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

Please see the attachment

Answer 2

Given :

The height of a triangle is decreased by 40% and its base is increased by 40%

To Find :

What will be the percentage change in its area

Solution:

Let the height of triangle be h and base of triangle be b

Area of triangle = $\frac{1}{2} \times base \times Height$

Area of triangle = $\frac{1}{2} \times b \times h=0.5bh$

Height of a triangle is decreased by 40%

New height = h-0.4h=0.6h

Its base is increased by 40%

New base = b+0.4b=1.4b

New Area = $\frac{1}{2} \times (0.6h) \times (1.4b)$

New Area = 0.42bh

Difference in areas = 0.5bh-0.42bh=0.08bh

Change percent =$\frac{0.08bh}{0.5bh} \times 100 = 16\%$

Hence the change in area percentage is 16%