Question

unit 4 test
score: gr 1.3
gr 5.3
gr 1.3
name:
period:
date
1
gr 1.3
select all the lengths that could be used to create the sides of a triangle.
□ 2, 3, 11
□ 37, 99, 63
□ 75, 24, 42
□ 13, 13, 13
□ 16, 32, 16

Explanation:

Step1: Apply triangle inequality theorem

For three side lengths \(a\), \(b\), \(c\) (\(a\leq b\leq c\)), the triangle inequality theorem states that \(a + b>c\).

Case1: \(a = 2\), \(b = 3\), \(c = 11\)

\(2+3=5<11\), so \(2\), \(3\), \(11\) cannot form a triangle.

Case2: \(a = 37\), \(b = 63\), \(c = 99\)

\(37 + 63=100>99\), so \(37\), \(99\), \(63\) can form a triangle.

Case3: \(a = 24\), \(b = 42\), \(c = 75\)

\(24+42 = 66<75\), so \(75\), \(24\), \(42\) cannot form a triangle.

Case4: \(a = 13\), \(b = 13\), \(c = 13\)

\(13+13=26>13\), so \(13\), \(13\), \(13\) (an equilateral triangle) can form a triangle.

Case5: \(a = 16\), \(b = 16\), \(c = 32\)

\(16+16=32\), since \(a + b=c\) (not \(a + b>c\)), \(16\), \(32\), \(16\) cannot form a triangle.

Answer:

\(37\), \(99\), \(63\) and \(13\), \(13\), \(13\)