Given the lengths of the sides of triangle ABC 2, 6, and 11 what is the perimeter and the area of ABC?
We are given the sides of the triangle ABC as 2, 6 and 11.
We see that the sum of the length of the sides with lengths 2 and 6, 2+ 6 = 8 is smaller than the length of the third side which is 11.
It is essential in a triangle for the sum of any two sides to be greater than the third side.
Therefore we cannot have a triangle with the sides 2, 6 and 11.
ABC cannot be a triangle.
the sum of two side of a triangle is always greater than the third side. this is one of the property of a triangle.
here the side are 2, 6 and 11
2+6 = 8< 11, so these cannot be a trianle.--[to be noted]
perimeter is the sum of the length of all the sides.
so the perimeter would be 2+6+11 = 19
So the are of the triangle would be
area of triangle = sqrt(s*(s-a)*(s-b)*(s-c))
This is known as heron's formula
s=semiperimeter = perimeter/2 :
a,band c are the sides of the triangle