Question

the following three sides could make a triangle: 8, 7 and 12 true false question 4 1 pts the following three sides could make a triangle: 21, 12 and 7 true false question 5 1 pts the following three sides could make a triangle: 12, 19 and 7 true false

Explanation:

Question (First Triangle: 8, 7, 12)

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: \(a + b>c\), \(a + c>b\), \(b + c>a\). Here, largest side is 12, smaller sides are 7 and 8.

Step2: Check \(7 + 8>12\)

Calculate \(7 + 8 = 15\). Since \(15>12\), and also \(7 + 12>8\) (19>8) and \(8 + 12>7\) (20>7), the sides satisfy the triangle inequality.

Step1: Identify Largest Side

Largest side is 21, smaller sides are 12 and 7.

Step2: Check \(12 + 7>21\)

Calculate \(12 + 7 = 19\). Since \(19<21\), the sum of the two smaller sides is not greater than the largest side, so it does not satisfy the triangle inequality.

Step1: Identify Largest Side

Largest side is 19, smaller sides are 12 and 7.

Step2: Check \(12 + 7>19\)

Calculate \(12 + 7 = 19\). The triangle inequality requires the sum to be strictly greater than the largest side, but here \(12 + 7 = 19\) (not greater), so it does not satisfy the inequality.

Answer:

True

Question 4 (Sides: 21, 12, 7)