Monthly Archives: August 2011

Ab Inequality

and are positive integers in the inequality . For how many different values of is there at least one value of that would make the inequality true? Source: mathcontest.olemiss.edu 2/5/2007 SOLUTION If , there exists such that If , there … Continue reading

Yellow Star

The four circles in the figure below each have a radius of 5 units. The centers of each circle form a square. If you use 3.14 as the approximate ratio of a circle’s circumference to its diameter, what is the … Continue reading

Two Isoceles Triangles

Two noncongruent triangles have the same area but different perimeters. Triangle A has sides lengths of 8, 8 and 6 cm. Triangle B has two sides with length of 8 cm. Find the length of the third side of Triangle … Continue reading

ABC Triangle

The perimeter of right triangle is cm. The altitude drawn to the hypotenuse is cm. What are the lengths of all three sides of the triangle? Source: mathcontest.olemiss.edu 10/9/2006 SOLUTION 3     4     5 6     8     10     [3 – 4 – … Continue reading

Roof Pitch

In construction, a roof with a 12 in 12 pitch means that the roof rises 12 feet vertically for every 12 feet of horizontal run. A 12 in 12 pitch roof forms a 45 degree base angle with the horizontal … Continue reading

Circles In Box

You have 20 congruent circles in a rectangle whose length is greater than its width. All circles are tangent at points of contact with other circles or the sides of the rectangle, as shown. The ratio of length to width … Continue reading

Difference of Perfect Squares

Which whole numbers can be expressed as the difference of two perfect squares? Source: NCTM Problem to Ponder 7/2011 SOLUTION The following spreadsheet displays the whole numbers that can be expressed as where and are whole numbers. The rows display the … Continue reading