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

aloha~! my name is zalgo and i am here to you out on this gracious day. in order to compare the ratios easily, it is best that we simplify the question first. so, the cougars would have 6 wins for 5 losses, bobcats make 2 wins for 1 loss. bulldogs and tigers have a ratio where you can't simplify it. so, the team with the lowest rate would be the bobcats.

i hope that this ! : d

"stay and stay proud! " - zalgo