# If the sides x,5,7 from a triangle then find how many integer value are possible for x?

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For a triangle with sides a, b and c it is essential that a+b>c, a+c>b and b+c>a.

The triangle that is given has sides x, 5, 7. The sides are related by x + 5 > 7 and 5 + 7 > x

=> x > 2 and 12 > x

The side x lies between 2 and 12. Also, as x has a integral value it can take on the values 3, 4, 5, 6, 7, 8, 9` `, 10 and 11.

**The value of x can be 3, 4, 5, 6, 7, 8, 9, 10 and 11**

The length of a side must be less than the sum of the other two sides. Here, that means x < 5+7, or x < 12.

In addition, remember that the length of a side must be greater than the difference of the other two sides. That means x > 7 - 5, or x > 2.

Therefore we have two limits for the value of x: 2 and 12.

2 < x < 12

Since x is an integer, x can be equal to numbers 3, 4, 5, 6, 7, 8, 9, 10, or 11 (the numbers that lie between 2 and 12 do NOT include 2 and 12). Remember that if we use 2 or 12 we will end up with overlapping straight lines, not a triangle.