Question

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manuel is building a frame for a triangular table. he has four pieces of wood measuring 8 feet, 3 feet, 5 feet, and 12 feet.
what pieces can manuel combine to make the frame?
manuel could only use the pieces that are 3 ft, 5 ft, and 12 ft in length.
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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 \(b + c>a\).

Check \(3\) ft, \(5\) ft, \(12\) ft

• \(3+5 = 8<12\), so these cannot form a triangle.

Check \(3\) ft, \(8\) ft, \(12\) ft

• \(3 + 8=11<12\), so these cannot form a triangle.

Check \(5\) ft, \(8\) ft, \(12\) ft

• \(5+8 = 13>12\)
• \(5 + 12=17>8\)
• \(8+12 = 20>5\)

Answer:

Manuel could only use the pieces that are \(8\) ft, \(5\) ft, and \(12\) ft in length.