Jeremiah is working on a model bridge. He needs to create triangular components, and he plans to use toothpicks. He finds three toothpicks of lengths 4 in., 5 in., and 1 in. Will he be

able to create the triangular component with these toothpicks without modifying any of the

lengths?

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