Q:

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. Question 3 options: 11.1 cm, 4.9 cm 44.4 cm, 3.2 cm 44.4 cm, 11.1 cm 24 cm, 4.9 cm

Accepted Solution

A:
Answer:The shortest possible length is 4.9 cmThe longest possible length is 11.1 cmThe answer is BStep-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 = 6/4Solve for x accordingly:7.4/x = 6/4(7.4)(4) = 6x29.6 = 6x4.93333... = xSo 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 = 4/67.4/x = 4/6(7.4)(6) = 4x44.4 = 4x11.1 = xThe longest possible length is 11.1 cm.