Question

ted has the following triangle dimensions.

• side length of 8
• side length of 14
• side length of 23

how many triangles can he construct?
he can construct three triangles. he can construct only one triangle.
he cannot construct a triangle. he can construct two triangles.

Explanation:

Step1: Apply triangle inequality theorem

For three side lengths \(a\), \(b\), \(c\) (where \(c\geq a\), \(c\geq b\)), the triangle inequality theorem states that \(a + b>c\). Let \(a = 8\), \(b = 14\), \(c = 23\). Then \(a + b=8 + 14=22\).

Step2: Compare the sum with the third side

Since \(22<23\) (i.e., \(a + b

Answer:

He cannot construct a triangle.