April 2017
Problem of the Month

from the International Singapore Maths Competition

The Area Number

In the diagram (not drawn to scale), the sloping line divides the area of the rectangle in the ratio 1 : 6.


What is the ratio a : b?
Show your work.

Solution to the Problem:

The ratio a:b = 2:5.

Let h = length of the rectangle.
The area of the triangle = 1/2 a h = 1   so ah = 2

The area of the rectangle = (a + b) h = 7   so ah + bh = 7
Subtracting, we get bh = 5

Therefore, ah / bh = a / b = 2 / 5

Correctly solved by:

1. Martin Round	Studley, Warwickshire, United Kingdom
2. James Alarie	Flint, Michigan
3. Vasilios Loutrianakis	Park Ridge,Illinois
4. Jonathan Spychalski	Park Ridge,Illinois
5. Madison Bindl	Mountain View High School, Mountain View, Wyoming
6. Amy Sorensen	Giddings High School, Giddings, Texas
7. Jim Hooker	Johnson City, Tennessee
8. Brijesh Dave	Mumbai city, Maharashtra, India
9. Claire Corbasson	Delta High School, Delta, Colorado

Send any comments or questions to: David Pleacher