Question

three side lengths are shown:
4 cm
3 cm
8 cm
how many triangles can be made using these sides lengths once each?
triangle(s) can be made.

Explanation:

Step1: Recall Triangle Inequality Theorem

The triangle inequality theorem states that for three side lengths \(a\), \(b\), and \(c\) (where \(c\) is the longest side), the sum of the two shorter sides must be greater than the longest side, i.e., \(a + b>c\).

Step2: Identify the sides and check the inequality

Here, the side lengths are \(3\) cm, \(4\) cm, and \(8\) cm. The longest side \(c = 8\) cm, and the two shorter sides are \(a = 3\) cm and \(b = 4\) cm.
Calculate the sum of the two shorter sides: \(3 + 4 = 7\) cm.
Now, compare this sum with the longest side: \(7\) cm \(< 8\) cm. Since the sum of the two shorter sides is not greater than the longest side, a triangle cannot be formed.

Answer:

\(0\)