Find the percentage increase in the area of a triangle if its each side is doubled??
Answers
Let a,b,c be the sides of the original A & s be its semi perimeter.
S= (a+b+c)/2
2s= a+b+c...
The sides of a new A are 2a, 2b, 2c
[ given: Side is doubled]
Let s' be the new semi perimeter.
s'= (2a+2b+2c)/2
s'= 2(a+b+c) /2
s'= a+b+c
S'= 2s.
(From eq 1.(2)
Let A= area of original triangle
A= vs(s-a)(s-b)(s-c.(3)
A'= area of new Triangle
A' = Vs'(s'-2a)(s'-2b)(s'-2c)
A'= v 2s(2s-2a)(2s-2b)(2s-2c)
[From eq. 2]
A'= v 2s×2(s-a)×2(s-b)×2(s-c)
= v16s(s-a)(s-b)(s-c)
A'= 4 vs(s-a)(s-b)(s-c)
A'= 4A.
(From eq (3)
Increase in the area of the triangle= A'- A= 4A - 1A= 3A
%increase in area= (increase in the area of the triangle/ original area of the triangle)x 100
% increase in area= (3A/A)×100
% increase in area= 3x100=300 %
Hence, the percentage increase in the area of a triangle is 300%
- SOLVED
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