August 2021
Problem of the Month

Triangle Problem



The sum of the lengths of the two legs of a right triangle is 20 cm.

What is the smallest possible length of the hypotenuse of this triangle?
Show your work!




Solution to the Problem:



There are two ways to approach this problem.

  1. You could draw a right triangle.   If you make one leg as small as possible, the other leg and the hypotenuse each approach 20 cm.
    This would be the largest value of the hypotenuse.
    So, if you make the two legs congruent, each leg equals 10 cm and the hypotenuse is 10 times the square root of 2 cm.   This would be the smallest value of the hypotenuse.

  2. The second method is to approach this as a maximum/minimum problem in calculus.






Correctly solved by:

1. Colin (Yowie) Bowey Beechworth, Victoria, Australia
2. Veena Mg Bangalore, Karnataka, India
3. Hari Kishan Meerut, Uttar Pradesh, India
4. Jonathan Punke Bremen High School,
Midlothian, Illinois
5. Sara Gagler Central High School,
Grand Junction, Colorado
6. Jordan Sollinger Woodridge High School,
Peninsula, Ohio
7. Kelly Stubblefield Mobile, Alabama
8. Ivy Joseph Pune, Maharashtra, India



Send any comments or questions to: David Pleacher