# The lengths of the sides of a triangle are 7 cm, 13 cm and 12 cm.

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The lengths of the sides of a triangle are 7 cm, 13 cm and 12 cm. Find the length of perpendicular from the opposite vertex to the side whose length is 12 cm.

answered Oct 4, 2018 by (-2,975 points)

Let, a = 7 cm, b = 13 cm, c = 12 cm

∴​  s = (a + b + c)/2  = (7 +13 +12)/2  = 32/2 = 16 cm

Area of ABC = under root(s(s -a) (s - b)(s -c))

=  under root(16(16 - 7)(16 - 13)(16 - 12)

=  under root(16 x 9 x 3 x 4 = 243 cm2

Also, Area of ABC =  1/2AC.BD

243 = 1/2 x 12 x BD   ⇒   BD = (243 x 2)/12

= 43 cm

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