Find the percentage increase in the area of a triangle if each side is increased by n times.
Answer:
100(n2−1)%
- Consider a △QRS with sides a,b and c. Let S=a+b+c2.
Area of △QRS,A1=√S(S−a)(S−b)(S−c) - Increasing the side of each side by n times, we get a new △XYZ.
△XYZ has sides na,nb and nc. - By Heron's formula:
Area of new triangle =√S1(S1−na)(S1−nb)(S1−nc)
Where, S1=na+nb+nc2=n×a+b+c2
- Increase in area =n2A1−A1
Increase in area .