Problem:
In the figure, the area of square WXYZ is 25 cm2. The four smaller squares have sides 1 cm long, either parallel to or coinciding with the sides of the large square. In â–³ABC, AB=AC, and when â–³ABC is folded over side BC, point A coincides with O, the center of square WXYZ. What is the area of â–³ABC, in square centimeters?
Answer Choices:
A. 415​
B. 421​
C. 427​
D. 221​
E. 227​
Solution:
Let M be the midpoint of BC. Since △ABC is isosceles, AM is an altitude to base BC. Because A coincides with O when △ABC is folded along BC, it follows that AM=MO=25​+1+1=29​ cm. Also, BC= 5−1−1=3 cm, so the area of △ABC is 21​⋅BC⋅AM=21​⋅3⋅29​=427​ cm2.
Answer: C​.
The problems on this page are the property of the MAA's American Mathematics Competitions
.jpg)