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  • On a board, there are 6 horizontal and 6 vertical lines that are parallel and equidistant from one another. What is the number of rectangles and squares that can be made?<div class='q

On a board, there are 6 horizontal and 6 vertical lines that are parallel and equidistant from one another. What is the number of rectangles and squares that can be made?

Option: 1

325


Option: 2

425


Option: 3

725


Option: 4

225


Answers (1)

best_answer

Given that,

There are 6 horizontal and vertical lines on a board.

For the selection of a rectangle or a square, we need to select 2 horizontal and 2 vertical lines.

Thus,

\mathrm{ \begin{aligned} & { }^6 C_2 \times{ }^6 C_2=\frac{6 !}{2 ! 4 !} \times \frac{6 !}{2 ! 4 !} \\ & { }^6 C_2 \times{ }^6 C_2=\frac{6 \times 5}{2} \times \frac{6 \times 5}{2} \\ & { }^6 C_2 \times{ }^6 C_2=15 \times 15 \\ & { }^6 C_2 \times{ }^6 C_2=225 \end{aligned} }

Therefore, the total number of ways to form the most rectangles and squares is 225 .

Posted by

Ajit Kumar Dubey

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