3. 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?
Answers
Answer:
Decreased by 16%
Step-by-step explanation:
Let the initial height be h and base be b.
Area = 1/2 height base = 0.5 bh
When height = h - 40% h = h - 0.4h = 0.6h and base = b + 40% b = b + 0.4b = 1.4b
Area of ∆ = 1/2 (0.6h)(1.4b) = 0.42 bh
% change = (change)/(initial) × 100%
% = (0.5bh - 0.42bh)/0.5bh x 100%
% = (0.08 bh)/(0.5 bh) x 100%
% = (0.08/0.5) x 100% = 16%
Given :-
If the height of a triangle is decreased by 40% and its base is increased by 40%,
To Find :-
Percentage change in its area?
Solution :-
Let the base be h and height be h
Height is decreased by 40%
h - 40% of h
h - 40/100 × h
h - 4h/10
10h - 4h/10
6h/10
Base increased by 40%
b + 40% of b
b + 40/100 × b
b + 4/10 × b
b + 4b/10
10b + 4b/10
14b/10
Now
Area = 1/2 × 6h/10 × 14b/10
Area = 1/2 × 0.6h × 1.4b
Area = 0.42bh
Now
Area of old triangle = 1/2 × b × h = 0.5bh
Difference between them = 0.5bh - 0.42bh = 0.08bh
Increase in % = 0.08/0.5 × 100
Increase in % = 16%
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