Question

A triangle has sides with lengths: 14, 9, and 2. How do you find the area of the triangle using Heron's formula?

Answer 1

This triangle is impossible to make.

Explanation:

Any triangle has a property that the sum of its any two sides is always greater than or equal to the third side.

Here let `a,b,c` denote the sides with `a=14`, `b=9` and `c=2`.

I will now find the sum of any two sides and will check that is the property satisfied.

`a+b=14+9=23`

This is greater than `c` which is the third side.

`a+c=14+2=16`

This is also greater than `b` which is the third side.

`b+c=9+2=11`

This is less than `a` which is the third side.

So the property for the given lengths is not satisfied therefore the given triangle can not be formed.