Question

the following three sides could make a triangle: 14, 10 and 9 true false question 7 1 pts the following three sides could make a triangle: 11, 22 and 9 true false question 8 1 pts the following three sides could make a triangle: 10, 7 and 12 true false

Explanation:

Question (First Triangle: 14, 10, 9)

Step1: Recall Triangle Inequality Theorem

For three side lengths \(a\), \(b\), \(c\) (where \(c\) is the largest side), the sum of the two smaller sides must be greater than the largest side. Here, the largest side is \(14\), and the other two are \(10\) and \(9\).

Step2: Check the inequality

Calculate the sum of the two smaller sides: \(10 + 9 = 19\). Now, compare \(19\) with \(14\). Since \(19>14\), the three sides satisfy the triangle inequality.

Step1: Recall Triangle Inequality Theorem

For side lengths \(11\), \(22\), \(9\), the largest side is \(22\). The two smaller sides are \(11\) and \(9\).

Step2: Check the inequality

Calculate the sum of the two smaller sides: \(11 + 9 = 20\). Now, compare \(20\) with \(22\). Since \(20<22\), the three sides do not satisfy the triangle inequality.

Step1: Recall Triangle Inequality Theorem

For side lengths \(10\), \(7\), \(12\), the largest side is \(12\). The two smaller sides are \(10\) and \(7\).

Step2: Check the inequality

Calculate the sum of the two smaller sides: \(10 + 7 = 17\). Now, compare \(17\) with \(12\). Since \(17>12\), the three sides satisfy the triangle inequality.

Answer:

True

Question (Second Triangle: 11, 22, 9)