Find the percentage increase in the area of a triangle if each side is increased to 55 times.


Answer:

2400%2400%

Step by Step Explanation:
  1. Consider a triangle QRSQRS with sides a,ba,b and c.c.
    Let S=a+b+c2S=a+b+c2
    Area of triangle QRS,A1=S(Sa)(Sb)(Sc)QRS,A1=S(Sa)(Sb)(Sc)
  2. Increasing the side of each side by 55 times, we get a new triangle XYZ.XYZ.
    XYZXYZ has sides 5a,5b5a,5b and 5c.5c.
    By Heron's formula,
    Area of new triangle =S1(S15a)(S15b)(S15c)=S1(S15a)(S15b)(S15c)
    Where S1=5a+5b+5c2=5×a+b+c2S1=5a+5b+5c2=5×a+b+c2
    Area of XYZ=5S(5S5a)(5S5b)(5S5c)XYZ=5S(5S5a)(5S5b)(5S5c)
    =54S(Sa)(Sb)(Sc)=52×A1=25A1
  3. Percentage increase in the area of the triangle, = Area of Triangle XYZ  Area of Triangle QRS Area of Triangle QRS×100=25A1A1A1×100=24A1A1×100=2400
  4. This means the area of the triangle, A1 is increased by 2400%.

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