Question

(pythagorean theorem lc)
can a triangle be formed with side lengths 13, 7, and 5? explain.
yes, because 13 + 7 > 5
yes, because 13 + 5 < 7
no, because 5 + 7 < 13
no, because 5 + 7 > 13

Explanation:

Step1: Recall the 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.

Step2: Check the sum of the two smaller sides

The two smaller sides are \(5\) and \(7\). Their sum is \(5 + 7=12\).

Step3: Compare with the largest side

The largest side is \(13\). Since \(12<13\) (i.e., \(5 + 7<13\)), a triangle cannot be formed.

Answer:

No, because \(5 + 7<13\)