Question

question 3 of 5
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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
8 ft, 3 ft, and 5 ft
3 ft, 5 ft, and 12 ft
8 ft, 5 ft, and 12 ft
8 ft, 3 ft, and 12 ft

Explanation:

Step1: Apply triangle inequality theorem

For three side lengths \(a\), \(b\), \(c\) (\(a\leq b\leq c\)), the triangle inequality theorem states that \(a + b>c\).

Case1: \(a = 3\), \(b = 5\), \(c = 8\)

\(3+5=8\), which does not satisfy \(a + b>c\) (since \(8 = 8\)).

Case2: \(a = 3\), \(b = 5\), \(c = 12\)

\(3 + 5=8<12\), which does not satisfy \(a + b>c\).

Case3: \(a = 5\), \(b = 8\), \(c = 12\)

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

Case4: \(a = 3\), \(b = 8\), \(c = 12\)

\(3+8=11<12\), which does not satisfy \(a + b>c\).

Answer:

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