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

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Answer 1 · 2016-01-20T19:30:54

This triangle is impossible to make.

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 $a, b, c$ $a,b,c$ denote the sides with $a = 14$ $a=14$ , $b = 9$ $b=9$ and $c = 2$ $c=2$ .

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

$a + b = 14 + 9 = 23$ $a+b=14+9=23$

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

$a + c = 14 + 2 = 16$ $a+c=14+2=16$

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

$b + c = 9 + 2 = 11$ $b+c=9+2=11$

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

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