an angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 4 cm long. a second side of the triangle is 7.4 cm long. find the longest and shortest possible lengths of the third side of the triangle. round answers to the nearest tenth of a centimeter.

The shortest possible length is 4.9 cm

The longest possible length is 11.1 cm

The answer is B

Step-by-step explanation:

You can solve this problem by applying the Angle Bisector Theorem.

Let's call the length we want to find "x". We need to find both the shortest possible length of x and the longest possible length of x.

To find the shortest possible length we can use 7.4/x = 6/4

Solve for x accordingly:

7.4/x = 6/4

(7.4)(4) = 6x

29.6 = 6x

4.93333... = x

So we can round this down to 4.9. The shortest possible length is 4.9 cm.

To find the longest possible length we can use 7.4/x = 4/6

7.4/x = 4/6

(7.4)(6) = 4x

44.4 = 4x

11.1 = x

The longest possible length is 11.1 cm.

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.