Can Two Rectangles Form a Disjoint Union of Six?

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In summary, a rectangle is a four-sided shape with four right angles and opposite sides that are equal in length and parallel to each other. To find the area of a rectangle, you multiply the length by the width using the formula A = l x w. The perimeter of a rectangle is found by adding up all four sides using the formula P = 2l + 2w. Two rectangles are considered similar if they have the same shape and their corresponding sides are proportional. Rectangles have various real-world applications in construction, design, and math, and are commonly used in computer graphics.
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Consider any two rectangles in the x-y plane. I have a book that asserts that the union of any two such rectangles is the DISJOINT union of AT MOST SIX rectangles. I've been sketching rectangles and simply can't come up with an example that demands SIX rectangles in the disjoint union. The most I can find is FIVE. Can someone come up with an example of two rectangles whose union is a disjoint union of six rectangles? Thanks!
 
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Is there no more information? Are the rectangles closed, open, etc?

What is your 5-rect solution?
 

FAQ: Can Two Rectangles Form a Disjoint Union of Six?

What is a rectangle?

A rectangle is a four-sided shape with four interior angles, all of which are right angles. The opposite sides of a rectangle are equal in length, and the opposite sides are parallel to each other.

How do you find the area of a rectangle?

To find the area of a rectangle, multiply the length by the width. The formula for the area of a rectangle is A = l x w, where A is the area, l is the length, and w is the width.

What is the perimeter of a rectangle?

The perimeter of a rectangle is the distance around the outside of the shape. To find the perimeter, add up all four sides of the rectangle. The formula for the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

How do you determine if two rectangles are similar?

Two rectangles are similar if they have the same shape but different sizes. This means that all the angles are equal and the corresponding sides are proportional to each other. To determine if two rectangles are similar, you can compare the ratios of their corresponding sides.

How can you use rectangles in the real world?

Rectangles are used in many real-world applications, such as building construction, furniture design, and packaging. They are also frequently used in math and geometry problems, and in computer graphics to create 2D shapes and images.

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