Question

determine if a triangle with the givin lengths can be formed. side lengths:3,13,15. If so classify it as acute,right, or obtuse

Answer 1

Solution

For this case we can name the lenghts like this:

a= 3

b= 13

c= 15

We need to satisfy that :

a+b >c

b+c > a

c+a > b

And we can verify that:

3+13 > 15

13+ 15 > 3

15+ 3 > 13

So therefore this triangle can exists

Since we dont satisfy the Pythegoras theorem given by.

$c^2=a^2+b^2$

Then this triangle is not a right triangle

And since:

c^2 > 13^2 +3^2

15^2 > 169 +9

225 > 169+9

Then the triangle needs to be obtuse