Question

1. does 8, 0, and 7 make a triangle?

a) yes, because 8 + 7 = 5 > 0
b) yes! 8 + 0 > 7
c) no, because 7 + 0 < 8
d) no! 7 + 8 < 0

Explanation:

Step1: Recall triangle inequality theorem

For three side lengths \(a\), \(b\), \(c\), the sum of any two sides must be greater than the third side. Let \(a = 8\), \(b=0\), \(c = 7\).

Step2: Check \(a + b>c\), \(a + c>b\), \(b + c>a\)

• \(a + b=8 + 0=8\), \(8>7\) (i.e., \(a + b>c\))
• \(a + c=8+7 = 15\), \(15>0\) (i.e., \(a + c>b\))
• \(b + c=0 + 7=7\), \(7<8\) (i.e., \(b + c

ot>a\))

Answer:

d. No, because \(7 + 0<8\)