March 2017
Problem of the Month

Rectangular Parallelepiped Problem
from the International Singapore Maths Competition

The areas of the faces of a rectangular box are 84 cm², 70 cm² and 30 cm².


What is the volume of the box?
Use algebra to solve the problem.

Solution to the Problem:

The answer is 420 cm³

Let x, y, and w represent the three length of the sides of the rectangular box.
Then you can write the following equations:
xy = 84
xw = 70
and yw = 30.

Then w = 70 / x and substitute it in equation 3 to obtain   70y / x = 30.
Solving for x, we get x = 70y / 30.
Substitute this in equation #1 to get   70y² / 30 = 84
This yields y² = 36, so y = 6 cm.
It follows that x = 14 cm and w = 5 cm.
Therefore, the volume is 6 x 14 x 5 = 420 cm³

Correctly solved by:

1. Christian Andersen	Mountain View High School, Mountain View, Wyoming
2. Jim Hooker	Johnson City, Tennessee
3. Rosemary Walker	Mountain View High School, Mountain View, Wyoming
4. James Alarie	Flint, Michigan
5. Martin Round	Studley, Warwicksire, United Kingdom
6. Kimberly Howe	Tuscaloosa, Alabama
7. Eliza Sheffield & Anna Vice	Tuscaloosa, Alabama
8. Sierra Toomer	Mountain View High School, Mountain View, Wyoming
9. SreeRoopa Sankararaman	Singapore, Singapore
10. Kylie Walker	Mountain View High School, Mountain View, Wyoming
11. Brijesh Dave	Mumbai city, Maharashtra, India
12. Braydon D. Saxton	Mountain View High School, Mountain View, Wyoming
13. Hope Pfeifer	Mountain View High School, Mountain View, Wyoming
14. Britan Woody	Mountain View High School, Mountain View, Wyoming

Send any comments or questions to: David Pleacher