Line AC = 3

Line CB =12

Line BA =?

ANSWER CHOICES

A) 3

B) 6

C) 9

D) 11

E) 12

F) 16

Line AC = 3

Line CB =12

Line BA =?

ANSWER CHOICES

A) 3

B) 6

C) 9

D) 11

E) 12

F) 16

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Westford, MA

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.

Middletown, CT

Hi Claudia;

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

AC=3

CB=12

a^{2}+b^{2}=c^{2}

3^{2}+12^{2}=c^{2}

9+144=c^{2}

153=c^{2}

√153=c

12.4=c

12=c

THE ANSWER IS E, IF MY ASSUMPTIONS ARE CORRECT.

Hallandale, FL

a = 12

b = 3

c = ?

15 > 3, 6, 9 , 11, 12.

(A, B, C, D, E)

12 + (

3 + 11 > 12 (D)

3 + 12 > 12 (E)

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