if the three segments below were used to form a triangle, what could the values for the length of the third side be? check all that apply.

Question

Line AC = 3

Line CB =12

Line BA =?

 

ANSWER CHOICES

A) 3

B) 6

C) 9

D) 11

E) 12

F) 16

Answer 1

Make believe you have a 12 inch stick and a 3 inch stick nailed together at one end (loose enough to be able to pivot).

 

How big a stick would you need to connect the other ends of the 12 and 3 inch sticks.

 

If the 3 inch stick is laying on top of the 12 inch stick you'd need just a 9 inch stick. But to make the combination a triangle the third stick would have to be a little bigger than 9 inches.

 

If the 3 inch stick is rotated 180º so it's collinear with the 12 inch stick but not laying on top of it, you'd now need a 15 inch stick to connect the ends. But to make the combination a triangle the third stick would have to be a little smaller than 15 inches.

 

So the third stick's length has to be constrained to: 9 < BA < 15.

 

Both D and E satisfy the constraints.

Answer 2

Rule for Δ ABC: any two sides added together must be greater than the third side.
If
   AB = c
   BC = a
   AC = b,
then
   a + b > c
   a + c > b
   b + c > a
~~~~~~~~~~~~

a = 12
b = 3
c = ?

1.)  12 + 3 > c
     
       15 > 3, 6, 9 , 11,  12.

(A, B, C, D, E)

2.)  12 + c > 3
    
      12 + (all choices) > 3

3.)  3 + c > 12

      3 + 11 > 12   (D)
      3 + 12 > 12   (E)

Thus, choices (D) and (E) satisfy all three conditions.

Answer 3

Hi Claudia;

I am assuming that BA is the hypotenuse opposite a 90-degree angle.

AC=3

CB=12

a²+b²=c²

3²+12²=c²

9+144=c²

153=c²

√153=c

12.4=c

12=c

 

THE ANSWER IS E, IF MY ASSUMPTIONS ARE CORRECT.