Determine if it is possible to form a triangle with side lengths 7 yd, 8 yd, and 9 yd.
Understand the Problem
The question asks whether it's possible to form a triangle given three side lengths: 7 yards, 8 yards, and 9 yards. To determine this, we need to verify if the sum of any two side lengths is greater than the third side length. This is known as the triangle inequality theorem.
Answer
Yes
Answer for screen readers
Yes, it is possible to form a triangle with side lengths 7 yards, 8 yards, and 9 yards.
Steps to Solve
- State the triangle inequality theorem
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
- Check if the sum of the first two sides is greater than the third side
We have sides with lengths 7, 8, and 9. Let's check if $7 + 8 > 9$:
$7 + 8 = 15$ $15 > 9$ This condition is satisfied.
- Check if the sum of the first and third sides is greater than the second side
Now let's check if $7 + 9 > 8$:
$7 + 9 = 16$ $16 > 8$ This condition is satisfied.
- Check if the sum of the second and third sides is greater than the first side
Finally, let's check if $8 + 9 > 7$:
$8 + 9 = 17$ $17 > 7$ This condition is satisfied.
- Conclusion
Since all three conditions are satisfied, it is possible to form a triangle with side lengths 7 yards, 8 yards, and 9 yards.
Yes, it is possible to form a triangle with side lengths 7 yards, 8 yards, and 9 yards.
More Information
A triangle with sides 7, 8 and 9 is an example of a scalene triangle, since all sides have different lengths.
Tips
A common mistake is only checking one or two combinations of sides instead of all three. All three possible combinations must satisfy the triangle inequality theorem for a triangle to be formed.
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