Area of a triangle is x1 sq units. If its sides are doubled, the area of the new triangle formed is x2 sq units. What is the percentage increase in the area?

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Feb 9, 2018

Answer:

# 300%#.

Explanation:

Suppose that, in #DeltaABC, BC=a, CA=b, AB=c#.

Also, let #[ABC]# denote the Area of #DeltaABC#.

Then, by Heron's Formula,

#[ABC]=sqrt(s(s-a)(s-b)(s-c)); s=(a+b+c)/2#.

Consider #DeltaA'B'C'# in which,

#B'C'=a'=2BC=2a, C'A'=2b, and A'B'=2c#.

Hence, #s'=(a'+b'+c')/2=(2a+2b+2c)/2=a+b+c=2s#.

#s'-a'=2s-2a=2(s-a)#.

Similarly, #s'-b'=2(s-b), and s'-c'=2(s-c)#.

#:.[A'B'C']=sqrt(s'(s'-a')(s'-b')(s'-c'))#,

#=sqrt(2s*2(s-a)*2(s-b)*2(s-c))#,

#=4sqrt(s(s-a)(s-b)(s-c))#.

#rArr [A'B'C']=4[ABC], or #

#x_2=4x_1#.

#:." The increase in the area="x_2-x_1=3x_1#.

#:." The % increase in the area="(x_2-x_1)/x_1*100#,

#=(3x_1)/x_1*100=300%#,

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