Monthly Archives: March 2013

Triangular Sandbox

A sandbox in the shape of an equilateral triangle is meters on each side. A fence is built around the triangular sandbox at a constant distance of meters. What is the number of square meters in the area between the … Continue reading

Posted in Problem solving | Tagged , , , , , | Leave a comment

1-7-24

Two numbers are such that their difference, sum, and their product are in the ratio of respectively. What is the product of the two numbers? Source: mathcontest.olemiss.edu 3/18/2013 SOLUTION Let be the two numbers. We are given the following proportion … Continue reading

Posted in Problem solving | Tagged , , , , | 1 Comment

23567

Find the sum of all positive three-digit integers formed from the five digits: , and . The same digit can appear more than once. Source: mathcontest.olemiss.edu 3/4/2013 SOLUTION Let’s try a smaller problem to get an idea of what’s going … Continue reading

Posted in Problem solving | Tagged , , , , , , , | 1 Comment

Circles Tangent to a Right Angle

In the figure, the two circles are tangent to the right angle and to one another. If the large circle has radius , what is the radius of the smaller circle? Source: NCTM Mathematics Teacher SOLUTION Let be the radius … Continue reading

Posted in Problem solving | Tagged , , , , , , , | Leave a comment

Silver Rectangle

A rectangle is called a silver rectangle if, when you remove two squares of side length equal to the height of the rectangle, the remaining rectangle is similar to the original rectangle. For instance, is similar to in the figure. … Continue reading

Posted in Problem solving | Tagged , , , , , , , | Leave a comment