An angle bisector of a triangle divides the opposite side of the triangle into segments 5 cm and 3 cm long. A second side of the triangle is 7.5 cm long. Find all possible lengths for the third side of the triangle. (Hint: draw a picture of the triangle, label one side with 7.5 cm, and solve for the other side. Then, move the 7.5 cm to the other side and solve.)
a.

12.5 cm or 4.2 cm

c.

4.5 cm or 12.5 cm
b.

11.6 cm or 4.2 cm

d.

4.5 cm or 11.6 cm

Question

An angle bisector of a triangle divides the opposite side of the triangle into segments 5 cm and 3 cm long. A second side of the triangle is 7.5 cm long. Find all possible lengths for the third side of the triangle. (Hint: draw a picture of the triangle, label one side with 7.5 cm, and solve for the other side. Then, move the 7.5 cm to the other side and solve.)
a.
	
12.5 cm or 4.2 cm
	
c.
	
4.5 cm or 12.5 cm
b.
	
11.6 cm or 4.2 cm
	
d.
	
4.5 cm or 11.6 cm

jdoe0001 · Answer

so... have you covered the pythagorean theorem yet?

directrix · Answer

You may need this theorem:

Triangle Angle Bisector Theorem:  If a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the sides that formed the angle.

directrix · Answer

x is to 7.5 as 5 is to 3

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