ABCD is a trapezoid. AB and CD are perpendicular to AD as shown in the diagram below.
Also AB + CD = BC. The length of AD = 7 units.
What is the product of AB and CD ?
Solution to the Problem:
(AB) (CD) = 49/4
Draw a line from B perpendicular to CD and call the foot of the perpendicular E.
Let x = CD and let y = AB.
So we are looking for x y.
CE = x - y
Use the Pythagorean Theorem to find CB:
(x - y)2 + 72 = (BC)2
Also we know that x + y = BC (given)
Substituting, we get
(x - y)2 + 72 = (x + y)2
Expanding, we get:
x2 -2xy + y2 + 49 = x2+ 2xy + y2
so, 4xy = 49
xy = 49/4
Click here for Carlos de Armas' excellent solution
Correctly solved by:
| 1. K. Sengupta | Calcutta, INDIA |
| 2. Davit Banana | Istanbul, Turkey |
| 3. Dr. Hari Kishan |
D.N. College, Meerut, Uttar Pradesh, India |
| 4. Rob Miles | Northbrook, Illinois, USA |
| 5. Sudhir Bavdekar | Mumbai, India |
| 6. Colin (Yowie) Bowey | Beechworth, Victoria, Australia |
| 7. Carlos de Armas | Barcelona City, Spain |
| 8. Seth Cohen | Concord, New Hampshire, USA |
| 9. Kelly Stubblefield | Mobile, Alabama, USA |