what wiil be the effect on the area of the triangle if its all sides are doubled and how?prove it.

Asked by  | 23rd Jul, 2008, 05:09: PM

Expert Answer:

 when the sides are doubled the area will be four times the original

 Let a , b, c  are the sides of the triangle  then the area A==  sq.rt of     s  (s-a) ) (s-b) (s-c) where s  = a+b+c /2

 if the sides  doubled  a1 = 2a . b1= 2b . c1 = 2c then   s1 = a1+b1+c1 / 2  ====> 2a +2b+2c  /2  == 2 ( a+b+c) / 2

                                                                                                                                                                           ==> 2 s

 therefore  s1 = 2s

 the new area A1=  sq.rt of s1 (s1-a1) ( s1-b1) ( s1 - c1)

                             ==> sq.rt of  2s  [[   (2s -2a ) (2s-2b) (2s -2c) ]]

                              ==> sq.rt of  2s .2x2x2 [[(s-a) (s-b) (s -c) ]]

                            ==> sq.rt of 2x2x2x2    s(s-a)(s-b) (s-c)

                            ==> 4  sq.rt of s (s-a)(s-b)(s-c)

                              ==>4 A

  therefore  A1  =  4A THAT IS  the area becomes  of the original

 

Answered by  | 24th Jul, 2008, 03:44: AM

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