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