# 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.
The text passage contains a mathematical word problem about creating a rectangular box from a sheet of metal, and it includes a solution to the problem.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 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.
user
The text passage contains a mathematical word problem about creating a rectangular box from a sheet of metal, and it includes a solution to the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER