Determine if it is possible to form a triangle with the given side lengths: 7 yd, 8 yd, 9 yd.
Understand the Problem
The question asks whether it's possible to construct a triangle given three side lengths: 7 yards, 8 yards, and 9 yards. To determine this, we need to check 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 construct a triangle with side lengths of 7 yards, 8 yards, and 9 yards.
Steps to Solve
- State the Triangle Inequality Theorem
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 7 and 8 is greater than 9
$7 + 8 > 9$ $15 > 9$. This condition is satisfied.
- Check if the sum of 7 and 9 is greater than 8
$7 + 9 > 8$ $16 > 8$. This condition is satisfied.
- Check if the sum of 8 and 9 is greater than 7
$8 + 9 > 7$ $17 > 7$. This condition is satisfied.
- Conclusion
Since all three conditions of the triangle inequality theorem are met, it is possible to construct a triangle with side lengths 7, 8, and 9.
Yes, it is possible to construct a triangle with side lengths of 7 yards, 8 yards, and 9 yards.
More Information
A triangle with sides 7, 8, and 9 would be an acute triangle, meaning all of its angles are less than 90 degrees.
Tips
A common mistake is forgetting to check all three possible combinations of sides. It's not enough to just check one or two combinations; all three must satisfy the triangle inequality theorem.
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