If the height of a triangle is decreased by 40% and it's base is increased by 40%, what will be the effect on its area ?
Answers
Answer:
Let the original base and height of the triabgke be b units and h units respectively. Then,
Original area = 1/2bh = 0.5bh
New base = b + 40% of b = 1.4b,
New height = h – 40% of h = 0.6h
Therefore, new area = 1/2 × 1.4b × 0.6h
= 0.84bh/2
= 0.42bh
Decrease in area = 0.5 bh – 0.42bh
= 0.08bh
Therefore, percent decrease
= 0.08bh/0.5bh × 100
= 16%
Given:-
- If the height of a triangle is decreased by 40% and it's base is increased by 40%.
To find:-
- what will be the effect on its area ?
Solution:-
Let height and base of the triangle be x and y .
=> 40 % of x=2x / 5
=> 40 % of y=2y / 5
Now ,
=> x′=x−2x / 5
=3x/ 5
=> y′=y+2y / 5
=7y/5
Therefore,
→ The new height is 3x/5 and the new base is 7y/5 .
⇒ Let : A=xy / 2 and A′= (3x/ 5 × 7x / 5 ) /2
→Dividing A by A′ , we get 25 / 21 .
→ Let the areas be 25 unit² and 21 unit² .
→Percent change =100(final−initial) / intial
→Therefore percent change in area
=100(21−25) / 25
= −16 %
Hence, area decreases by 16 %.
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