Problem:
In the figure shown below, choose point D on side BC so that â–³ACD and â–³ABD have equal perimeters. What is the area of â–³ABD?
Answer Choices:
A. 43​
B. 23​
C. 2
D. 512​
E. 25​
Solution:
Because the perimeters of â–³ADC and â–³ADB are equal, CD=3 and BD=2.
△ADC and △ADB have the same altitude from A, so the area of △ADC will be 3/5 of the area of △ABC, and △ADB will be 52​ of the area of △ABC. The area of △ABC is 21​⋅3⋅4=6, so the area of △ADB is 52​⋅6=12/5.
Answer: D​.
The problems on this page are the property of the MAA's American Mathematics Competitions
