Math, asked by Anonymous, 10 months ago

2nd questions answer fast plsss

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Answered by karan9051
0
Plz write your question
properly

Anonymous: the question is if each side of triangle is increased by 2 times then how many times triangle area increase
Answered by rathibhagwati3
0

Answer:


Step-by-step explanation:

Let a,b,c be the sides of the triangle.


Perimeter 2s = a + b + c

Semi-perimeter, s = (a+b+c)/2

Using Heron's formula:

Area of the triangle A = √s(s−a)(s−b)(s−c)


Now, if the sides are doubled: 2a, 2b, 2c


Let s' be the semi-perimeter.

2s' = 2a + 2b + 2c

s' = a + b + c

or s' = 2s


Area of the triangle, A' = √s′(s′−2a)(s′−2b)(s′−2c)

A' = √(2s)(2s−2a)(2s−2b)(2s−2c)

A' = √24s(s−a)(s−b)(s−c)

A' = 4√s(s−a)(s−b)(s−c)

A' = 4A

A':A = 4:1


The area of triangle increases 4 times.

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