Given the lengths of the sides of triangle ABC 2, 6, and 11 what is the perimeter and the area of ABC?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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.

chaobas's profile pic

chaobas | College Teacher | (Level 1) Valedictorian

Posted on

Now,

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

 

 

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