text: # Thread: Rectangular box
  
  1. ## Rectangular box
  
  A rectangular box is to be made from a rectangular piece of shee metal 20in wide and 30in long by cutting a square piece of equal size from each of the corners and bending up the sides so that they make a 90 degree angle with the base. The base of the finished box will be 200 square inches. About how many inches high will the box be?
  
  2. Originally Posted by sarahh
  A rectangular box is to be made from a rectangular piece of shee metal 20in wide and 30in long by cutting a square piece of equal size from each of the corners and bending up the sides so that they make a 90 degree angle with the base. The base of the finished box will be 200 square inches. About how many inches high will the box be?
  Let x be the length of one side of one of the squares you have to cut off.
  
  Then you get:
  
  $\displaystyle (20-2x)(30-2x) = 200$ ......... Expand the brackets. You'll get aquadratic equation:
  
  $\displaystyle 4x^2-100x+400 = 0$ ......... Solve this equation for x. Only one of the two solutions is valid with your problem.
  
  (For confirmation only: x = 5)
  
  3. Why do we reject the 20 answer again?
  
  4. Originally Posted by sarahh
  Why do we reject the 20 answer again?
  Plug in the solution into the original equation:
  
  $\displaystyle \begin{array}{ccc}(20-2 \cdot 20)(30-2 \cdot 20)& = &200\\\\ (-20)(-10)&=&200 \end{array}$
  
  That means you cut off more than there exists. In my opinion quite impossible but the modern science ...
  
  5. Ahh that does make sense. Many thanks earboth!
  Sarah H.
explanation: The document is a thread from a forum discussing a math problem about constructing a rectangular box from a sheet of metal. It includes the initial problem statement, a detailed solution, and a follow-up question with an explanation. The thread contains a question and an answer.
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distilabel_metadata.content: # Thread: Rectangular box
  
  1. ## Rectangular box
  
  A rectangular box is to be made from a rectangular piece of shee metal 20in wide and 30in long by cutting a square piece of equal size from each of the corners and bending up the sides so that they make a 90 degree angle with the base. The base of the finished box will be 200 square inches. About how many inches high will the box be?
  
  2. Originally Posted by sarahh
  A rectangular box is to be made from a rectangular piece of shee metal 20in wide and 30in long by cutting a square piece of equal size from each of the corners and bending up the sides so that they make a 90 degree angle with the base. The base of the finished box will be 200 square inches. About how many inches high will the box be?
  Let x be the length of one side of one of the squares you have to cut off.
  
  Then you get:
  
  $\displaystyle (20-2x)(30-2x) = 200$ ......... Expand the brackets. You'll get aquadratic equation:
  
  $\displaystyle 4x^2-100x+400 = 0$ ......... Solve this equation for x. Only one of the two solutions is valid with your problem.
  
  (For confirmation only: x = 5)
  
  3. Why do we reject the 20 answer again?
  
  4. Originally Posted by sarahh
  Why do we reject the 20 answer again?
  Plug in the solution into the original equation:
  
  $\displaystyle \begin{array}{ccc}(20-2 \cdot 20)(30-2 \cdot 20)& = &200\\\\ (-20)(-10)&=&200 \end{array}$
  
  That means you cut off more than there exists. In my opinion quite impossible but the modern science ...
  
  5. Ahh that does make sense. Many thanks earboth!
  Sarah H.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a thread from a forum discussing a math problem about constructing a rectangular box from a sheet of metal. It includes the initial problem statement, a detailed solution, and a follow-up question with an explanation. The thread contains a question and an answer.
  
  Label: question-and-answer