Question

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

Answer 1

Solution:-
Let the base and height of the triangle be 'b' and 'h' respectively.
So, the original area of the triangle = 1/2× b × h = 1/2bh
Now, according to the question.
New area of the triangle = 1/2 × (b + 40 % of b) × (h - 40 % of h)
= 1/2 × (b + 40b/100) × (h - 40h/100)
= 1/2 × (140b/100) × (60h/100)
= 1/2 × (7b/5) × (3h/5)
= (21bh/50)  
Now, change in the area = New area - original area 
= 21bh/50 - 1/2bh
= - 4bh/50
Therefore, the percentage change in the area = (Change in area*100)/Original area
⇒ {(- 4bh/50)*100}/(1/2bh)
= - 16 %
Therefore, the area will decrease by 16 %.
Answer.