Math, asked by itzkanika85, 4 months ago

Find the percentage increase in the area of a triangle if its each side is doubled??​

Answers

Answered by Itzsmartlywartly3435
2

Answer:

Semi-perimeter of the triangle, s=2a+b+c

Area of triangle  =s(s−a)(s−b)(s−c). 

When each side is doubled, the new sides are 2a,2b,2c. 

Hence, new s′=22a+2b+2c=2(2a+b+c)=2s

New area A′=2s(2s−2a)(2s−2b)(2s−2c)

=2×2×2×2×s(s−a)(s−b)(s−c)

=4s(s−a)(s−b)(s−c). 

∴ % change in Area =AA′−A×100

=s(s−a)(s−b)(s−c)4s(s−a)(s−b)(s−c)−s(s−a)(s−b)(s−c)

Hope It Helps u✌

Answered by Anonymous
7

300%

Semi-perimeter of the triangle, s=

2

a+b+c

Area of triangle =

s(s−a)(s−b)(s−c)

.

When each side is doubled, the new sides are 2a,2b,2c.

Hence, new s

=

2

2a+2b+2c

=2(

2

a+b+c

)=2s

New area A

=

2s(2s−2a)(2s−2b)(2s−2c)

=

2×2×2×2×s(s−a)(s−b)(s−c)

=4

s(s−a)(s−b)(s−c)

.

∴ % change in Area =

A

A

−A

×100

=

s(s−a)(s−b)(s−c)

4

s(s−a)(s−b)(s−c)

s(s−a)(s−b)(s−c)

×100

=

1

4−1

×100

=300%

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