Find the area of a triangle whose perimeter is 180 cm and 2 of its sides are 80 cm and 18 cm. Also, calculate the altitude of the triangle corresponding to the shortest side.

Given that the Perimeter of the triangle is 180 cm.

Let the length of sides be a, b, and c.

Also, two sides are given as 80 cm and 18 cm.

∴ Let a = 80 cm, b = 18 cm.

Now perimeter of triangle = a + b + c

∴ a + b + c = 180

⇒ 80 + 18 + c = 180

⇒ c = 82cm

∴ sides of triangle are a = 80cm, b = 18cm, c = 82cm.

∴ 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 trsiangle is 720cm².

We need to calculate the altitude of the triangle corresponding to the shortest side.

∴ The shortest side will act as a base

Shortest side = b = base = 18 cm

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

=

=

∴ Altitude =

∴ The altitude of the triangle corresponding to the shortest side is 80 cm.