Math Problem Statement

The image contains a problem involving a square with side length 6 units. It provides several statements regarding the maximum number of non-overlapping shapes that can fit inside the square. Here are the statements: 1. The maximum number of non-overlapping squares with a side length of 2 units that can fit inside the square is 9. 2. The maximum number of non-overlapping squares with a side length of 1 unit that can fit inside the square is 35. 3. The maximum number of non-overlapping rectangles with a length of 2 units and breadth of 3 units that can fit inside the square is 6. 4. The maximum number of non-overlapping rectangles with a length of 2 units and breadth of 3 units that can fit inside the square is 5.

Solution

It seems you've uploaded a file. Let me take a look at the image and extract the necessary information to assist you with your question. PIL import Image

Load and display the image

image_path = '/mnt/data/1733462853776uje37b82.jpg' img = Image.open(image_path) img.show()I have displayed the image you uploaded. I will now analyze its contents and provide you with a detailed response.It appears that I need to extract and interpret the information from the image. Let me process it and help you with your query. pytesseract

Use pytesseract to extract text from the image

extracted_text = pytesseract.image_to_string(img)

Display the extracted text

extracted_textThe image contains a problem involving a square with side length 6 units. It provides several statements regarding the maximum number of non-overlapping shapes that can fit inside the square. Here are the statements:

  1. The maximum number of non-overlapping squares with a side length of 2 units that can fit inside the square is 9.
  2. The maximum number of non-overlapping squares with a side length of 1 unit that can fit inside the square is 35.
  3. The maximum number of non-overlapping rectangles with a length of 2 units and breadth of 3 units that can fit inside the square is 6.
  4. The maximum number of non-overlapping rectangles with a length of 2 units and breadth of 3 units that can fit inside the square is 5.

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Math Problem Analysis

Mathematical Concepts

Area
Geometry
Tiling
Optimization

Formulas

Area of square = side^2
Area of rectangle = length × breadth

Theorems

Tiling theorem
Maximizing non-overlapping shapes within a fixed area

Suitable Grade Level

Grades 6-8