Question

Mr. Littles is building a triangular sandbox using three boards. He already has two boards that measure 9 feet and 12 feet. Select all of the values that could represent the length of the third board of his triangular sandbox.

Answer 1

• 9 feet, 15 feet, 19 feet

Explanation:

Options are:

• 2 feet
• 3 feet
• 9 feet
• 15 feet
• 19 feet
• 21 feet
• 30 feet

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Use the triangle inequality theorem: sum of any two side must be greater than the third side by length

• 2 feet ⇒ no, as 2 + 9 < 12
• 3 feet ⇒ no, as 3 + 9 = 12
• 9 feet ⇒ yes
• 15 feet ⇒ yes
• 19 feet ⇒ yes
• 21 feet ⇒ no, as 9 + 12 = 21
• 30 feet ⇒ no, as 9 + 12 < 30