Find the percentage increase in the area of a triangle if each side is increased by nn times.


Answer:

100(n21)%100(n21)%

Step by Step Explanation:
  1. Consider a QRSQRS with sides a,ba,b and c.c. Let S=a+b+c2S=a+b+c2.
    Area of QRS,A1=S(Sa)(Sb)(Sc)QRS,A1=S(Sa)(Sb)(Sc)
  2. Increasing the side of each side by nn times, we get a new XYZXYZ.
    XYZXYZ has sides na,nbna,nb and ncnc.
  3. By Heron's formula:
    Area of new triangle =S1(S1na)(S1nb)(S1nc)=S1(S1na)(S1nb)(S1nc)
    Where, S1=na+nb+nc2=n×a+b+c2S1=na+nb+nc2=n×a+b+c2
     Area of XYZ=nS(nSna)(nSnb)(nSnc)=n4S(Sa)(Sb)(Sc))=n2×A1
  4. Increase in area =n2A1A1=n2A1A1
    % Increase in area =A1(n21)A1100= 100(n21)%.

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