Question

Determine if 7, 8, and 13 can be the lengths of the sides of a triangle. If yes, classify the triangle.

A.

Yes, it is an acute triangle.
B.

Yes, it is an obtuse triangle.
C.

Yes, it is a right triangle.
D.

No, it cannot be a triangle.

Answer 1

\(\large c^2 = a^2 + b^2 - 2ab \cos (C)\)


that gives :

\(c^2\gt a^2 +b^2 \implies \text{obtuse}\)
\(c^2\lt a^2 +b^2 \implies \text{acute}\)
\(c^2= a^2 +b^2 \implies \text{right}\)

Answer 2

Is \(13^2 > 7^2 + 8^2\) ?

Answer 3

yes 169 is greater than 113

Answer 4

so is it B?

Answer 5

thats right !
but how are you sure that the given lengths indeed form a triangle ?

Answer 6

they could be so small that you wont be able to join the other two sides, to close the shape, right ?

Answer 7

right

Answer 8

you need to check if the given lengths satisfy ALL below conditions :
\(a+b < c\)
\(b+c < a\)
\(c+a< b\)

Answer 9

In words : `sum of any TWO sides must be greater than the third side`

Answer 10

Oh yeah i remember that

Answer 11

good :) B is correct btw ! good job !!

Answer 12

@ganeshie8 Thank You