Complete the inequality so that it represents the whole-number values that side a could be to create a triangle.
C=7
b=6
<a<
1 < a < 7
is that correct?
To create a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Using this rule, we can write the inequality as:
a + b > C
Substituting the given values, we get:
a + 6 > 7
Subtracting 6 from both sides, we get:
a > 1
Therefore, the complete inequality is:
1 < a < 7
This means that side a can be any whole number between 1 and 7 (excluding 1 and 7) to create a triangle with sides of lengths a, b, and C.
To create a triangle, the sum of any two sides must be greater than the third side. In this case, the inequality becomes:
a + b > C
Substituting the given values:
a + 6 > 7
Now, to isolate "a," we subtract 6 from both sides:
a > 7 - 6
Simplifying:
a > 1
So the incomplete inequality is:
1 < a
To determine the range of values for side a to create a triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, we have:
C = 7
b = 6
Using the theorem, we know that:
a + b > C
Substituting in the values we have:
a + 6 > 7
To solve for a, we isolate it on one side of the inequality:
a > 7 - 6
Simplifying the expression:
a > 1
Therefore, the inequality representing the whole-number values that side a could be to create a triangle is:
a > 1
To determine the range of possible values for side a to create a triangle, we can use the triangle inequality theorem, which states that for a triangle with sides a, b, and c, the sum of any two sides must be greater than the third side.
In this case, we have c = 7 and b = 6.
The inequality for side a, using the triangle inequality theorem, is:
c + b > a
Substituting the given values:
7 + 6 > a
13 > a
Therefore, the inequality that represents the whole-number values that side a could be to create a triangle is:
a < 13