text: # The perpendicular dropped from the top of the rectangle divides its diagonal into segments
  
  The perpendicular dropped from the top of the rectangle divides its diagonal into segments of 9 cm and 16 cm. Calculate the area of the rectangle
  
  1. Vertices of the rectangle A, B, C, D. AC – diagonal. BH is the height drawn to the diagonal.
  
  AH = 9 centimeters. CH = 16 centimeters.
  
  2. The length of the height BH, drawn from the vertex of the right angle of the triangle ABC, is calculated
  
  according to the formula:
  
  BH = √AN x CH = √9 x 16 = √144 = 12 centimeters.
  
  3. AC = AH + CH = 9 + 16 = 25 centimeters.
  
  4. Calculate the area of ​​the triangle ABC:
  
  AC x BH / 2 = 25 x 12/2 = 150 centimeters².
  
  5. The diagonal of the rectangle divides it into two equal triangles ABC and ACD.
  
  6. With this in mind, we calculate the area (S) of the rectangle:
  
  S = 150 x 2 = 300 centimeters².
  
  Answer: The area of ​​a rectangle is 300 centimeters².
  
  One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
explanation: The document contains a math problem and its solution. The problem involves calculating the area of a rectangle given the segments of its diagonal when a perpendicular is dropped from the top. The solution is provided step-by-step, leading to the final answer of 300 centimeters². The document also includes a brief unrelated paragraph about the importance of education.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # The perpendicular dropped from the top of the rectangle divides its diagonal into segments
  
  The perpendicular dropped from the top of the rectangle divides its diagonal into segments of 9 cm and 16 cm. Calculate the area of the rectangle
  
  1. Vertices of the rectangle A, B, C, D. AC – diagonal. BH is the height drawn to the diagonal.
  
  AH = 9 centimeters. CH = 16 centimeters.
  
  2. The length of the height BH, drawn from the vertex of the right angle of the triangle ABC, is calculated
  
  according to the formula:
  
  BH = √AN x CH = √9 x 16 = √144 = 12 centimeters.
  
  3. AC = AH + CH = 9 + 16 = 25 centimeters.
  
  4. Calculate the area of ​​the triangle ABC:
  
  AC x BH / 2 = 25 x 12/2 = 150 centimeters².
  
  5. The diagonal of the rectangle divides it into two equal triangles ABC and ACD.
  
  6. With this in mind, we calculate the area (S) of the rectangle:
  
  S = 150 x 2 = 300 centimeters².
  
  Answer: The area of ​​a rectangle is 300 centimeters².
  
  One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math problem and its solution. The problem involves calculating the area of a rectangle given the segments of its diagonal when a perpendicular is dropped from the top. The solution is provided step-by-step, leading to the final answer of 300 centimeters². The document also includes a brief unrelated paragraph about the importance of education.
  
  Label: question-and-answer