Q9 of 14 Page 206

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.

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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