Question

Plz Help
A. Yes
B. No
c. Maybe
D. Can4 be determined

Answer 1

Answer: A) Yes

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Step-by-step explanation:

Convert each mixed number to decimal form

`2 (1)/(2) = 2 + (1)/(2) = 2 + 0.5 = 2.5\\\\3 (1)/(4) = 3 + (1)/(4) = 3 + 0.25 = 3.25\\\\5 (1)/(8) = 5 + (1)/(8) = 5 + 0.125 = 5.125\\\\`

We have the three potential sides of a = 2.5, b = 3.25 and c = 5.125

For a triangle to be possible with these side lengths, the following three inequalities must all be true

• a+b > c
• a+c > b
• b+c > a

Which is due to the triangle inequality theorem.

In other words, we should be able to add any two sides to get a result larger than the third side.

• a+b = 2.5+3.25 = 5.75 is larger than c = 5.125, so a+b > c is true.
• a+c = 2.5+5.125 = 7.625 is larger than b = 3.25, so a+c > b is true.
• b+c = 3.25+5.125 = 8.375 is larger than a = 2.5, so b+c > a is true.

All three inequalities mentioned are true when (a,b,c) = (2.5, 3.25, 5.125)

Therefore, a triangle is possible with these side lengths.