Question

7. The length of sides of a triangle are 7 cm, 12 cm & 13 cm.Find the
length of perpendicular from opposite vertex to the side whose
length is 12 cm.
4​

Answer 1

Answer:

4√3 cm.

Step-by-step explanation:

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 = 24√3 cm2

Also, Area of △ABC =  1/2AC.BD

24√3 = 1/2 x 12 x BD   ⇒   BD = (24√3 x 2)/12  

= 4√3 cm

Hence, the length of perpendicular is 4√3 cm.

Answer 2

Answer:

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 = (√s(s -a) (s - b)(s -c))

= (√16(16 - 7)(16 - 13)(16 - 12)

= (√16 x 9 x 3 x 4

= 24√3 cm2

Also, Area of △ABC = 1/2AC.BD

24√3 = 1/2 x 12 x BD

=BD = (24√3 x 2)/12

= 4√3 cm