Answer:
No, he would not be able to create a triangle without modifying the lengths of the toothpick
Step-by-step explanation:
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
