Monthly Archives: December 2017

Largest Equilateral Triangle in a Square

How long is the side of the largest equilateral triangle that can be inscribed in a square with side length ? Source: NCTM Mathematics Teacher, August 2006 Solution A first guess is an equilateral triangle of side length . Could … Continue reading

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

Third Root of Equation

Two of the roots of the equation are and . Find the third root of the equation. Source: NCTM Mathematics Teacher, August 2006 Solution Let be the third root of the equation. We write the equation in factored form Multiply … Continue reading

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

Partial Fractions

When is decomposed into partial fractions (fractions that sum to the given fraction), what is the sum of the numerators when each fraction is reduced to lowest terms? Source: NCTM Mathematics Teacher, August 2006 Solution Solving for Collecting like terms … Continue reading

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

Equilateral Triangle and Square

A pentagon made up of equilateral triangle with side length on top of square is inside a circle passing through points , and . Find the radius of the circle. Source: NCTM Mathematics Teacher, August 2006 Solution Let be the … Continue reading

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

Children Sharing Money

Al, Bee, Cecil, and Di have , and , respectively. Their father proposed that Al and Bee share their wealth equally, and then Bee and Cecil do likewise, and then Cecil and Di. Their mother’s plan is the same except … Continue reading

Posted in Problem solving | Tagged , | Leave a comment

Cottages on a Straight Road

There are four cottages on a straight road. The distance between Ted’s and Alice’s cottages is km. Both Bob’s and Carol’s cottages are twice as far from Alice’s as they are from Ted’s. Find the distance between Bob’s and Carol’s … Continue reading

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