Problem: The perimeter of an isosceles right triangle is 2p. Its area is:
Answer Choices:
A. (2+2​)p
B. (2−2​)p
C. (3−22​)p2
D. (1−22​)p2
E. (3+22​)p2
Solution:
Let x be one of the equal sides of the triangle. 2p=2x+x2​;
∴x=2+2​2p​,A=21​x2=21​⋅6+42​4p2​⋅6−42​6−42​​=p2(3−22​)