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Question

The percentage increase in the area of a triangle if its each side is doubled, is

A
200%
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B
300%
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C
400%
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D
500%
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Solution

The correct option is B 300%
Let a, b, c be the sides of the original triangle & s be its semi perimeter.
S, a+b+c/2
2s.a+b+c ……………..(1)
The sides of a new triangle 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 equation (1)) …………..(2)
Let Δ= area of original triangle
Δ=s(sa)(sb)(sc) …………(3)
Δ=area of new triangle
Δ=s(s2a)(s2b)(s2c)
Δ=2s(2s2a)(2s2b)(2s2c)
From equation- (2)
Δ=2s.2(sa)2.(sb)2(sc)
Δ=16s(sa)(sb)(sc)
Δ=4s(sa)(sb)(sc)
Δ=4Δ
Increase in the area of the triangle =ΔΔ
=4Δ1Δ
=3Δ.
% increase in are = (increase in the area of the triangle/ original area of the triangle)×100
% incomes in area =3Δ/Δ×100
% increase in area =3×100
% increase in area =300%
Hence the percentage increase in the area of a triangle is 300%.
So, the answer is B. 300%.

1221376_1450801_ans_30047f1d337a421c9140d82ba4b34236.jpg

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