Question

1. which combination of measurements could form a triangle? 41m, 30m, 15m; 8m, 10m, 20m; 25m, 25m, 75m; 8m, 2.5m, 2.5m

Explanation:

Step1: Recall Triangle Inequality Theorem

For three side lengths \(a\), \(b\), \(c\) to form a triangle, the sum of any two sides must be greater than the third side: \(a + b>c\), \(a + c>b\), \(b + c>a\).

Step2: Check Option 41m, 30m, 15m

• \(30 + 15=45>41\)
• \(41 + 15=56>30\)
• \(41 + 30=71>15\)

All inequalities hold.

Step3: Check Option 8m, 10m, 20m

• \(8 + 10 = 18<20\), so it fails the triangle inequality.

Step4: Check Option 25m, 25m, 75m

• \(25+25 = 50<75\), fails the triangle inequality.

Step5: Check Option 8m, 2.5m, 2.5m

• \(2.5+2.5 = 5<8\), fails the triangle inequality.

Answer:

A. 41m, 30m, 15m