Answer:
The answer is No, according to the Triangle Theorem.
Step-by-step explanation:
When you have the sides of the triangle, you must be able to add up 2 sides and have a larger number than the other side.
4+5 = 9 which is greater than 1
5+1 = 6 which is greater than 4
4+1=5 which is equal but not greater than 5
No, he would not be able to create a triangle without modifying the lengths of the toothpick
In order to determine if the toothpicks can be used to create the triangle, make use of the Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
the square of the longest side of the triangle should be equal to the sum of the square of the two shortest sides
4² + 1²
16 + 1 = 15
5² = 25
15 is not equal to 25
So the lengths cannot be used
the 1 in length would need to be extended by 2 inches to be used
To confirm
3² + 5²
16 + 9 = 25
This is correct
In conclusion, in order to determine if the lengths can be used, check with Pythagoras theorem. If the lengths can be used, the square of the longest side of the triangle should be equal to the sum of the square of the two shortest sides
To learn more about Pythagoras theorem, please check: https://brainly.com/question/24417148?referrer=searchResults
