Math, asked by ishaanx, 6 months ago

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

Answers

Answered by ashwathi93
0

Answer:

Hope this answer helped you.☺️

Step-by-step explanation:

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%.

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