Permutations and combinations - is square a rectangle?

Thread starter AdityaDev
Start date Dec 8, 2014
Tags

combinations geometry permutations rectangle square

In summary, squares are a special type of rectangle with equal sides, and the number of permutations and combinations of squares and rectangles can be calculated using nPr and nCr. A square and a rectangle can have the same number of combinations if they have the same dimensions, and permutations and combinations are used in various real-life scenarios involving squares and rectangles. Additionally, a square and a rectangle can have the same perimeter if their sides are equal in length.

Dec 8, 2014

AdityaDev

I was going through a p and c problem where I had to find the number of non congruent RECTANGLES.
Answer includes number of squares as well.
SHOULD SQUARE BE TAKEN AS A RECTANGLE?

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Dec 8, 2014

HallsofIvy

Science Advisor

Homework Helper

Yes, a square is a special kind of rectangle.

Of course, I cannot guarantee that whoever set this problem will agree with me!

1. Are squares considered rectangles?

Yes, squares are considered a special type of rectangle with equal sides. Every square is a rectangle, but not every rectangle is a square.

2. How do you calculate the number of permutations and combinations of squares and rectangles?

The number of permutations and combinations of squares and rectangles can be calculated using the formula nPr and nCr, where n is the total number of items and r is the number of items in each permutation or combination. For example, if there are 4 squares and 3 rectangles, the number of possible combinations would be 7C3.

3. Can a square have the same number of combinations as a rectangle?

Yes, a square and a rectangle can have the same number of combinations if they have the same number of sides and the same dimensions. For example, a 3x3 square and a 3x3 rectangle would have the same number of combinations.

4. How do permutations and combinations apply to squares and rectangles in real life?

Permutations and combinations are used in various real-life scenarios involving squares and rectangles, such as in combinatorial game theory, packing problems, and designing rectangular structures. They are also used in fields like architecture, engineering, and computer science.

5. Can a square and a rectangle have the same perimeter?

Yes, a square and a rectangle can have the same perimeter if their sides are equal in length. For example, a 4x4 square and a 2x6 rectangle would both have a perimeter of 16 units.