How do you use Heron's formula to find the area of a triangle with sides of lengths #12 #, #5 #, and #7 #?

1 Answer
Jan 21, 2016

The given numbers cannot be lengths of sides of a triangle. (The area is zero)

Explanation:

The Heron's formula says that for any triangle with sides #a,b,c# its area is #A=sqrt(p(p-a)(p-b)(p-c))#, where #p=(a+b+c)/2#

If we substitute given numbers we see, that:

#p=(12+5+7)/2=12#, so

#A=sqrt(12*0*7*5)=0#

You should have noticed, that given numbers cannot be the lengths of sides of a triangle, because #12=7+5# and according to triangle inequalities each side must be smaller then the sum of remaining sides