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 5 in., 5 in.. and 2 in. Will he be able to create the triangular component with these toothpicks without modifying any of the lengths?
Yes, according to the Triangle Sum Theorem
Yes, according to the Triangle Inequality Theorem
O No, according to the Triangle Sum Theorem
O No, according to the Triangle Inequality Theorem

(C) Yes, according to the Triangle Inequality Theorem

Step-by-step explanation:

The lengths of three toothpicks are

a= 5 in.

b= 5 in.

c= 2 in.

As the lengths of three toothpicks are given, so, check the possibility of forming a triangle by the Triangle Inequality Theorem.

According to Triangle Inequality Theorem,  the sum of the length of any two sides must be greater than the third side.

Check all possible combination sum of two sides, we have

a+b=5+5= 10 in., which is greater than c=2 in.

so, a+b>c ...(i)

Similarly,

a+c=5+2=7 in., which is greater than b=5 in.

So, a+c>b ...(ii)

And b+c=5+2=7 in., which is greater than a=5 in.

So, b+c>a ...(iii)

Equations (i), (ii), and (iii) satisfied the Triangle Inequality Theorem.

So, yes, he will be able to create the triangular component with these toothpicks.

Hence, option (C) is correct.

Step-by-step explanation:

Given lengths:

As per Triangle Inequality Theorem, the sum of side length  of any two sides must be greater than the side length of the third side

Verifying:

So the answer is yes

m∠a is 90°

m∠b is 40°

the opening of this porabola is facing up

step-by-step explanation: