Question

10 determine if the side lengths could form a triangle. 15 m, 8 m, 10 m

Explanation:

Step1: Apply triangle inequality theorem

The triangle inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), the following must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\). Let \(a = 8\), \(b = 10\), and \(c = 15\).
First, check \(a + b>c\): \(8+10 = 18\), and \(18>15\).

Step2: Check other inequalities

Check \(a + c>b\): \(8 + 15=23\), and \(23>10\).
Check \(b + c>a\): \(10+15 = 25\), and \(25>8\).

Answer:

Since all three inequalities \(8 + 10>15\), \(8+15>10\), and \(10 + 15>8\) are satisfied, the side lengths \(15m\), \(8m\), and \(10m\) can form a triangle.