jmc

Question

In the diagram, triangles ABC and CBD are isosceles. The perimeter of CBD is 19, the perimeter of ABC is 20, and the length of BD is 7. What is the length of AB? FIGURE

Accepted Answer

In ABC, ABC= BAC, so AC=BC. In BCD, CBD= CDB, so CD=BC. Since the perimeter of CBD is 19 and BD=7, then 7+BC+CD=19 or 2(BC)=12 or BC=6. Since the perimeter of ABC is 20, BC=6, and AC=BC, then AB+6+6=20 or AB=8. So our final answer is 8.