CBSE Class 9 Answered
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