Q. 93.8( 4 Votes )

# In a triangle ABC AB = 15 cm BC = 13 cm and AC = 14 cm. Find area of triangle ABC and hence its altitude on AC.

Answer :

Let the sides be AB = a = 15cm,

BC = b = 13cm and,

AC = c = 14cm.

∴ Sides of triangle are a = 15cm, b = 13cm, c = 14cm.

∴ **By Heron’s formula we get area of triangle**

**=**

(where **s =** s is called as the semi perimeter )…(1)

∴ we get

Substituting the value of s, a, b and c in equation 1 we get

⇒

=

=

∴ The area of a triangle is.

The altitude on AC,

∴ AC = c = 14

Now the area of a triangle having base and altitude is given by

=

=

∴ Altitude =

∴ Altitude = 16.92cm

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