Answer :

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 720cm^{2}.

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.

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