Leo has three straws. They are 4 inches, 8 inches, and 10 inches long. Can he make a triangle using these three straws?
Option 1 = Yes
Option 2 = No
(1 point)
Option
is the correct answer.
Option 1 is the correct answer.
According to 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.
In this case, 4 + 8 = 12, which is greater than 10. Similarly, 4 + 10 = 14, which is greater than 8, and 8 + 10 = 18, which is greater than 4.
Hence, Leo can make a triangle using these three straws.
explain
Sure! The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In other words, if you have three line segments and the sum of the lengths of any two is greater than the length of the third, then you can construct a triangle using those line segments.
In this scenario, Leo has three straws with lengths of 4 inches, 8 inches, and 10 inches. To determine if Leo can make a triangle using these straws, we need to check if the sum of the lengths of any two straws is greater than the length of the third.
Let's check:
4 + 8 = 12 (greater than 10)
4 + 10 = 14 (greater than 8)
8 + 10 = 18 (greater than 4)
Since the sum of the lengths of any two straws is greater than the length of the third, Leo can indeed make a triangle using these three straws. Therefore, Option 1, "Yes", is the correct answer.
To determine if Leo can make a triangle using these three straws, we can apply the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check if this condition holds true for Leo's straws:
1. The sum of the lengths of the 4-inch straw and the 8-inch straw is 4 + 8 = 12 inches. This is greater than the length of the 10-inch straw.
2. The sum of the lengths of the 4-inch straw and the 10-inch straw is 4 + 10 = 14 inches. This is also greater than the length of the 8-inch straw.
3. Finally, the sum of the lengths of the 8-inch straw and the 10-inch straw is 8 + 10 = 18 inches. This is greater than the length of the 4-inch straw.
Since the sum of the lengths of any two sides is greater than the length of the third side in all cases, Leo can indeed make a triangle using these three straws.
Therefore, the correct answer is option 1: Yes.