April 2022
Problem of the Month

Rectangle Problem
from Terry Schlagel

ABCD and AEBF are rectangles
with AE = 1 and EB = 2.

What is the area of ABCD and what are its dimensions?
Show your work.

Solution:

The area of rectangle ABCD is 2 square units.
The dimensions are sqrt(5) by 2 / sqrt(5) or approximately 2.236 by .8944.

Use the Pythagorean Theorem to solve for AB: 1² + 2² = AB²



Now substitute the value of x in the expressions for AD and BC and check if they are equal.
Then multiply AD x AB to get the area of ABCD.

Correctly solved by:

1. Ritwik Chaudhuri	Santiniketan, West Bengal, India
2. Veena Mg	Bangalore, Karnataka, India
3. Davit Banana	Istanbul, Turkey
4. Jonathan Punke	Bremen High School, Midlothian, Illinois
5. Cash Henrie	Mountain View High School, Mountain view, Wyoming
6. Ivy Joseph	Pune, Maharashtra, India
7. K. M. Thomas	Mumbai, Maharashtra, India
8. Dr. Hari Kishan	D.N. College, Meerut, Uttar Pradesh, India
9. Indianna Covington	Mountain View High School, Mountain view, Wyoming
10. Colin (Yowie) Bowey	Beechworth, Victoria, Australia

Send any comments or questions to: David Pleacher