Question

brian cut 3 wooden sticks to use as the sides of a triangle. which list below could be the lengths, in feet, of the sticks brian cut?

• 5ft, 10ft, 15ft
• 3ft, 4ft, 5ft
• 4ft, 4ft, 8ft
• 5ft, 2ft, 10ft

Explanation:

To determine if three lengths can form a triangle, we use the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the remaining side.

Step1: Check 5ft, 10ft, 15ft

Check the sums:

• \(5 + 10 = 15\), but \(15\) is not greater than \(15\) (it's equal). So, this does not satisfy the triangle inequality.

Step2: Check 3ft, 4ft, 5ft

Check the sums:

• \(3 + 4 = 7\), and \(7>5\)
• \(3 + 5 = 8\), and \(8>4\)
• \(4 + 5 = 9\), and \(9>3\)

All sums satisfy the triangle inequality.

Step3: Check 4ft, 4ft, 8ft

Check the sums:

• \(4 + 4 = 8\), but \(8\) is not greater than \(8\) (it's equal). So, this does not satisfy the triangle inequality.

Step4: Check 5ft, 2ft, 10ft

Check the sums:

• \(5 + 2 = 7\), and \(7<10\). So, this does not satisfy the triangle inequality.

Answer:

3ft, 4ft, 5ft