¶ 1995 AMC8 Problem 24
Problem:
In parallelogram is the altitude to the base and is the altitude to the base . [Note: Both pictures represent the same parallelogram.] If and , then
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since opposite sides of a parallelogram are equal, . Then . Using the Pythagorean Theorem gives , and then also. The area of a parallelogram is base altitude. Using base and altitude gives an area of . Using base and altitude must also give an area of . Thus .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions