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

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given that the height of triangle is decreased by 40%
• Base is increased by 40%

To Find:

• We have to find the percentage change in the area of given triangle

Solution:

Let us assume :

Initially height of triangle = h

Initially the length of base = b

Initially Area = (1/2)(bh)

_____________________________

When height is decreased by 40%

Final height = h - 40%h

Final height = h - 0.4h

Final height = 0.6h

h' = 0.6 h

_______________________

When length of base is increased by 40%

Final length of base = b + 40%b

Final length of base = b + 0.4b

Final length of base = 1.4b

b' = 1.4 b

________________________

Final area = (1/2).b'.h'

Final area = (1/2)(1.4b)(0.6h)

Final area = 0.84(1/2)(bh)

_____________________________

Change in area = Intial - Final

Change = 0.16(1/2)(bh)

Percentage change can be calculated

Percentage change = $\dfrac{change}{initial} \times 100$

Percentage change = $\dfrac{0.16(1/2)(bh)}{(1/2)(bh)}\times100$

Percentage change = 0.16 x 100

Percentage change = 16%

Hence the area will also get decreased by 16%