# Tag Archives: square

## Round Table

A round table can be made square by dropping the four leaves. If a side of a square table measures inches, to the nearest hundredth of a square inch, how much smaller is the area of the table when the … Continue reading

## 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

## 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

## Two Squares

If the vertices of square are the midpoints of the edges of square , then what is the ratio of the area of square to square ? Source: NCTM Mathematics Teacher, September 2006 Solution The diagonal of square divides square … Continue reading

## Area of a Disc

If the area of a disc inscribed in a square is square centimeters, what is the area of the square? Source: NCTM Mathematics Teacher, September 2006 Solution Area of disc = Area of square = Answer: square centimeters

## Length of Side of Square

If the numerical value of the area of a square plus two times the numerical value of its perimeter is equal to , what is the length of one side of the square? Source: NCTM Mathematics Teacher, September 2006 Solution … Continue reading

## Rectangle Inside a Square

An isosceles right triangle is removed from each corner of a square piece of paper so that a rectangle remains. What is the length of a diagonal of the rectangle if the sum of the areas of the removed pieces … Continue reading

## Absolute Value Function

What is the area of the region bounded by the graph of ? Source: NCTM Mathematics Teacher, October 2006 Solution If and If and If and If and The four graphs intersect and form a square of side length . … Continue reading

## Vertices of a Square

If and are the coordinates of two opposite vertices of a square, what are the coordinates of the other two vertices? Source: NCTM Mathematics Teacher, October 2006 Solution Let and be the two given opposite vertices of the square. The … Continue reading

## Volumes of Two Cubes

The combined volumes of two cubes with integer side lengths are numerically equal to the combined lengths of their edges. What are the dimensions of the cubes? Source: NCTM Mathematics Teacher, January 2006 Solution Suppose is the side length of … Continue reading