Which sets of measurements could be the side lengths of a triangle? Select each correct answer. A \( 4 \mathrm{~cm}, 8 \mathrm{~cm}, 13 \mathrm{~cm} \) B \( 3 \mathrm{~cm}, 3 \mathrm{~cm}, 3 \mathrm{~cm} \) C \( 6 \mathrm{~cm}, 7 \mathrm{~cm}, 8 \mathrm{~cm} \) D a \( 7 \mathrm{~cm}, 7 \mathrm{~cm}, 10 \mathrm{~cm} \) E \( 5 \mathrm{~cm}, 9 \mathrm{~cm}, 14 \mathrm{~cm} \)
Real Tutor Solution
Answer
Solution
Reviewed and approved by the UpStudy tutoring team
Extra Insights
To determine whether sets of measurements can form a triangle, you can use the Triangle Inequality Theorem. This theorem states that the sum of any two side lengths must be greater than the third side length. So, let's break down the options and see which sets fit the bill! B \(3 \text{ cm}, 3 \text{ cm}, 3 \text{ cm}\): All sides are equal, so they certainly form an equilateral triangle! C \(6 \text{ cm}, 7 \text{ cm}, 8 \text{ cm}\): The sum of every pair of sides is greater than the third side (6+7 > 8, 6+8 > 7, 7+8 > 6), making this a valid triangle as well! D \(7 \text{ cm}, 7 \text{ cm}, 10 \text{ cm}\): This forms an isosceles triangle, as the two sides are equal and the Triangle Inequality Theorem holds. Now, A \(4 \text{ cm}, 8 \text{ cm}, 13 \text{ cm}\) and E \(5 \text{ cm}, 9 \text{ cm}, 14 \text{ cm}\) do not meet the requirement since \(4 + 8 = 12\) (less than 13) and \(5 + 9 = 14\) (not strictly greater). So, A and E fall flat in their quest to be triangles! In summary, the sets that can make triangles are B, C, and D—everyone else can hit the road!