# A triangle has sides with lengths: 7, 2, and 14. How do you find the area of the triangle using Heron's formula?

Mar 27, 2018

No area

#### Explanation:

The triangle has no area, and it cannot exist.

The triangle inequality states that,

$a + b > c$

$b + c > a$

$c + a > b$

In words, the sum of a triangle's two sides' lengths is always bigger than the remaining one.

But here, we get: $7 + 2 = 9 < 14$, and so this triangle cannot exist.

Mar 27, 2018

color(brown)("We can not form a triangle with the given measurements."

#### Explanation: Given : $a = 7 , b = 2 , c = 14$

To find the area of the triangle using Heron's Formula.

Heron's Formula ${A}_{t} = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)} \text{ , where } s = \frac{a + b + c}{2}$

$s = \frac{7 + 2 + 14}{2} = 11.5$

color(red)("For a triangle to exist, sum of any two sides must be greater than the third side"

In this case, $a + b < c$.

color(brown)("Hence, we can not form a triangle with the given measurements."