Atriangle has two sides of lengths 7 and 12. what value could the length of the third side be? check all that apply.
a.)9
b.)5
c.)7
d.)3
e.)11
f.)17

A)

C)

E)

F)

Step-by-step explanation:

we know that

The Triangle Inequality Theorem, states  that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

Let

a,b,c ------>  the length sides of the triangle

in this problem we have

Applying the triangle inequality theorem

1)

-------> -----> inequality A

2)

------->   ------> inequality B

The solution for the length of the third side is the interval----->

------> compound system of inequalities

we're going to verify all the cases

If a value could be the length of the third side, then the value must be satisfy  the compound system of inequalities

case A)

Substitute the value in the compound system of inequalities

For

 -------> is true

therefore

The value of   can be the length of the third side

case B)

Substitute the value in the compound system of inequalities

For

 -------> is not true

therefore

The value of   cannot be the length of the third side

case C)

Substitute the value in the compound system of inequalities

For

 -------> is true

therefore

The value of   can be the length of the third side

case D)

Substitute the value in the compound system of inequalities

For

 -------> is not true

therefore

The value of   cannot be the length of the third side

case E)

Substitute the value in the compound system of inequalities

For

 -------> is true

therefore

The value of   can be the length of the third side

case F)

Substitute the value in the compound system of inequalities

For

 -------> is true

therefore

The value of   can be the length of the third side

step-by-step explanation:

i'm pretty sure it would take 20 hours because it's half the men so you multiply the number of hours it takes by 2