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4 equidistant vertical lines are drawn on board 4 equidistant horizontal lines are also drawn on the board cutting the 4 vertical lines, and the distance between any two consecutive horizontal lines is equal to that between any two consecutive vertical lines. What is the maximum number of squares thus formed?
- a)20
- b)34
- c)14
- d)8
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
4 equidistant vertical lines are drawn on board 4 equidistant horizon...
Single square boxes.
Single square boxes along a horizontal row = 3
Single square boxes along a vertical row = 3
Number of single square boxes = 3 × 3 = 9
Case II: Double square boxes = double square box along horizontal X double square box along vertical = 2 × 2 = 4
Case III: Triple square boxes = 1 × 1 = 1
∴ Total number of squares = 9 + 4 + 1 = 14
Most Upvoted Answer
4 equidistant vertical lines are drawn on board 4 equidistant horizon...
To solve this problem, let's break it down step by step:
1. Understanding the given information:
- There are 4 equidistant vertical lines drawn on a board.
- There are 4 equidistant horizontal lines drawn on the board, cutting the vertical lines.
- The distance between any two consecutive vertical lines is equal to the distance between any two consecutive horizontal lines.
2. Visualizing the lines:
To better understand the problem, let's visualize the lines on the board using a grid:
```
| | | |
-+-----+-----+-----+-
| | | |
-+-----+-----+-----+-
| | | |
-+-----+-----+-----+-
| | | |
-+-----+-----+-----+-
```
Here, the vertical lines are represented by "|" and the horizontal lines by "-".
3. Counting the squares:
To find the maximum number of squares formed, we need to determine all the possible combinations of squares that can be formed using these lines.
- 1x1 Squares: We can see that each intersection of a vertical and horizontal line forms a 1x1 square. So, there are 4x4 = 16 such squares.
- 2x2 Squares: We can observe that there are 3x3 = 9 possible 2x2 squares formed by the intersections of the lines.
- 3x3 Squares: There are 2x2 = 4 possible 3x3 squares.
- 4x4 Squares: There is only 1 possible 4x4 square.
Therefore, the total number of squares formed is 16 + 9 + 4 + 1 = 30.
4. Analyzing the options:
We are given a list of options to choose from: 20, 34, 14, and 8.
We can see that none of the options match our calculated result of 30 squares. Hence, none of the given options is correct.
However, if we assume that the given options are incorrect and calculate the maximum number of squares, we find that the correct answer is 30 squares (as calculated in step 3).
1. Understanding the given information:
- There are 4 equidistant vertical lines drawn on a board.
- There are 4 equidistant horizontal lines drawn on the board, cutting the vertical lines.
- The distance between any two consecutive vertical lines is equal to the distance between any two consecutive horizontal lines.
2. Visualizing the lines:
To better understand the problem, let's visualize the lines on the board using a grid:
```
| | | |
-+-----+-----+-----+-
| | | |
-+-----+-----+-----+-
| | | |
-+-----+-----+-----+-
| | | |
-+-----+-----+-----+-
```
Here, the vertical lines are represented by "|" and the horizontal lines by "-".
3. Counting the squares:
To find the maximum number of squares formed, we need to determine all the possible combinations of squares that can be formed using these lines.
- 1x1 Squares: We can see that each intersection of a vertical and horizontal line forms a 1x1 square. So, there are 4x4 = 16 such squares.
- 2x2 Squares: We can observe that there are 3x3 = 9 possible 2x2 squares formed by the intersections of the lines.
- 3x3 Squares: There are 2x2 = 4 possible 3x3 squares.
- 4x4 Squares: There is only 1 possible 4x4 square.
Therefore, the total number of squares formed is 16 + 9 + 4 + 1 = 30.
4. Analyzing the options:
We are given a list of options to choose from: 20, 34, 14, and 8.
We can see that none of the options match our calculated result of 30 squares. Hence, none of the given options is correct.
However, if we assume that the given options are incorrect and calculate the maximum number of squares, we find that the correct answer is 30 squares (as calculated in step 3).
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4 equidistant vertical lines are drawn on board 4 equidistant horizontal lines are also drawn on the board cutting the 4 vertical lines, and the distance between any two consecutive horizontal lines is equal to that between any two consecutive vertical lines. What is the maximum number of squares thus formed?a)20b)34c)14d)8Correct answer is option 'C'. Can you explain this answer?
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