Tag Archives: square

Square of 111,111,111

Find the exact value of . Source: NCTM Mathematics Teacher, February 2008 Solution Answer: Alternative solution Multiply the numbers manually using the old-fashioned multiplication algorithm. It should be straightforward because there is no “carry”. Advertisements

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Four Congruent Rectangles

Four congruent rectangles are arranged as shown in the figure to form a large rectangle. The area of the large rectangle is . What is the area of a square that has the same perimeter as the large rectangle? Source: … Continue reading

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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

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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

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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

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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

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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

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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

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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

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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

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