A triangle has sides with lengths: 6, 9, and 15. How do you find the area of the triangle using Heron's formula?

2 Answers

Area of triangle is zero

Explanation:

In general, a triangle will exist only when the sum of two sides is greater than the longest side.

The longest side of given triangle 1515 is equal to the sum of other two sides 66 & 99 thus triangle will be a straight line or triangle does not exist.

Now, the semi-perimeter ss of triangle with the sides a=6a=6, b=9b=9 & c=15c=15

s=\frac{a+b+c}{2}=\frac{6+9+15}{2}=15s=a+b+c2=6+9+152=15

The area of triangle by using Herio's formula

\Delta=\sqrt{s(s-a)(s-b)(s-c)}

=\sqrt{15(15-6)(15-9)(15-15)}

=0

The area of the triangle will be zero

Jul 12, 2018

Triangle Inequality Theorem :

"The sum of the lengths of any two sides of a triangle"

"must be greater than the length of the third side."

Explanation:

Let ,

a=6 ,b=9 and c=15

=>6+9=15=>color(red)(a+b=c

So, according to Triangle Inequality Theorem ,

""color(red)"it is not possible to construct a triangle."

OR

:." Semi perimeter of triangle is :"

s=(a+b+c)/2=(6+9+15)/2=15

So,

s-a=15-6=9 ,s-b=15-9=6 ,s-c=15-15=0

"Using"color(blue)" Heron's formula :" "area of the triangle is :"

Delta=sqrt(s(s-a)(s-b)(s-c))

=>Delta=sqrt(15(9)(6)(0))=0

So the given length of sides can not forms triangle .