If each side is doubled, then the percentage increase in the area of a
triangle, is
[ ]
a) 2009
b) 3005
c) 400% d) 500%
Answers
Answer:
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(s−a)(s−b)(s−c)
…………(3)
Δ
′
=area of new triangle
Δ
′
=
s
′
(s
′
−2a)(s
′
−2b)(s
′
−2c)
Δ
′
=
2s(2s−2a)(2s−2b)(2s−2c)
From equation- (2)
Δ
′
=
2s.2(s−a)2.(s−b)2(s−c)
Δ
′
=
16s(s−a)(s−b)(s−c)
Δ
′
=4
s(s−a)(s−b)(s−c)
Δ
′
=4Δ
Increase in the area of the triangle =Δ
′
−Δ
=4Δ−1Δ
=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%.
300 %
Step-by-step explanation:
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