SOLUTION: In Triangle PQR, the length of side QR is 12 and the length of side PR is 20. What is the greatest possible integer length of side PQ. A. 9 B. 16 C. 25 D. 27 E. 31 How

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Question 647533: In Triangle PQR, the length of side QR is 12 and the length of side PR is 20. What is the greatest possible integer length of side PQ.
A. 9
B. 16
C. 25
D. 27
E. 31
How do I find this out? Thanks.
Answer by swincher4391(1107) (Show Source):
You can put this solution on YOUR website!
You could actually physically see this, but the two smallest sides must add up to more than the third. This is called the triangle inequality.
Notice that if x<12, x is the smallest side.
If . 12 is the smallest side.
If x>20, 12 is the smallest side.
So really for x>12, 12 is the smallest side.
Case 1: x<12
Then x+12 > 20
x>8 and since we're only talking about integer lengths,
Case 2:
Then 12 + x < 20
Same as case 1.

Case 3: x>20
12+20 > x
x < 32 or
So our possible values range from 9 to 31.
31 is the largest, and it is the answer.
E.