Question

sides of a triangle practice
complete this assessment to review what youve learned. it will not count toward your gra
leo has three straws. they are 4 inches, 8 inches, and 10 inches long. can he make a triangle using these three straws?
option 1 = yes
option 2 = no
(1 point)

Explanation:

Step1: Recall triangle inequality theorem

The triangle inequality theorem states that for three side lengths \(a\), \(b\), and \(c\) (where \(c\) is the longest side), the sum of the two shorter sides must be greater than the longest side, i.e., \(a + b>c\).

Step2: Identify the sides

Here, the side lengths are \(4\) inches, \(8\) inches, and \(10\) inches. The longest side \(c = 10\) inches, and the two shorter sides \(a = 4\) inches and \(b = 8\) inches.

Step3: Check the inequality

Calculate the sum of the two shorter sides: \(4 + 8=12\) inches. Now, compare this sum with the longest side: \(12>10\). Also, we should check the other inequalities (though for the longest side being the limiting factor, if \(a + b>c\), the other inequalities \(a + c>b\) and \(b + c>a\) will also hold as \(c\) is the largest). For \(a + c\): \(4+10 = 14>8\), and for \(b + c\): \(8 + 10=18>4\). Since all triangle inequalities are satisfied, a triangle can be formed.

Answer:

Option 1 = Yes