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

2 Answers
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:

https://www.onlinemathlearning.com/area-triangle.html

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 (s-a) (s-b) (s-c)) " , where " s = (a + b + c) / 2#

#s = (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."#