Problem:
In rhombus ABCD, point P lies on segment AD such that BP⊥AD,AP=3, and PD=2. What is the area of ABCD?
Answer Choices:
A. 35​
B. 10
C. 65​
D. 20
E. 25
Solution:
The side length of the rhombus is AP+PD=5, so AB=5. The Pythagorean Theorem applied to △BPA yields BP=4. Thus the area of ABCD is 5⋅4=(D)20​.
The problems on this page are the property of the MAA's American Mathematics Competitions
