Question

marlena has 3 straws. two straws have the lengths shown. she does not know the length of the shortest straw, but when she forms a triangle with all three, the triangle is obtuse. which are possible lengths of the shortest straw? check all that apply. 5 inches 6 inches 7 inches 8 inches 9 inches

Explanation:

Step1: Apply triangle inequality

For three side lengths \(a\), \(b\), \(c\) (\(a\leq b\leq c\)), \(a + b>c\). Let the unknown side be \(x\) (\(x\leq9<12\)), then \(x + 9>12\), so \(x>3\).

Step2: Use obtuse - triangle condition

For an obtuse triangle with side lengths \(a\), \(b\), \(c\) (\(a\leq b\leq c\)), \(a^{2}+b^{2}

Answer:

5 inches, 6 inches, 7 inches