Question

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 ?​

Answer 1

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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Answer 2

Answer:

Decreases by 16 percent.