A triangle has one side that is 5 inches long and another that is 7 inches long. How many different lengths, in inches,are possi
ble for the last side of the triangle?
1 answer:
Answer:
2 < c < 12
Step-by-step explanation:
Let the last side of the triangle = c
The sum of any two sides must be greater than the third side. Let's say we have triangle ABC, where a = 5 inches and b = 7 inches
a + b > c (1)
a + c > b (2)
b + c > a (3)
From (1);
a + b > c
7 + 5 > c
c < 12
From (2):
a + c > b
7 + c > 5
7 - 5 < c
c > 2
From (3):
b + c > a
5 + c > 7
c > 7 - 5
c > 2
So the possible lengths of c are: 2 < c < 12
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