Question 1138605: A rectangular sheet of tin is 15cm long and 9cm wide. A uniform strip is to be cut off around the sheet. The examining area is 112cm squared. Calculate the width of the strip. The answer is 0.5 cm.
What I have got so far: At - As = 112
At = 135
135 - As = 112
23 = As
23 = (15-2x) (9-2x)
4x^2 - 12x + 28
4(x^2 -12x +28)
x=14
Found 4 solutions by ikleyn, ankor@dixie-net.com, josgarithmetic, greenestamps:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
What is "examining area" ?
This term is not defined in the problem, and this fact momentarily makes the problem DEFECTIVE.
True Math problem does not allow an ambiguous interpretation.
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To see many similar solved problems, that are your samples and templates, look into the lessons
- Problems on the area and the dimensions of a rectangle surrounded by a strip
- Cynthia Besch wants to buy a rug for a room
- Problems on a circular pool and a walkway around it
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic
"Dimensions and the area of rectangles and circles and their elements".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! A rectangular sheet of tin is 15cm long and 9cm wide. A uniform strip is to be cut off around the sheet. The examining area is 112cm squared. Calculate the width of the strip. The answer is 0.5 cm.
What I have got so far: At - As = 112
At = 135
135 - As = 112
I have corrected as follows
112 = (15-2x) (9-2x)
4x^2 - 30x - 18x + 135 = 112
4x^2 - 48x + 135 - 112 = 0
4x^2 - 48x + 23 = 0
Two solutions, found by the quadratic equation a=4; b=-48, c=23
x=11.5
and the more reasonable solution is
x=.5 cm
Answer by josgarithmetic(39617)  (Show Source):
You can put this solution on YOUR website! ---------------------------------------
Calculate the width of the strip.
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No. You mean something else.
Calculate the uniform width of the area surrounding the cut sheet on tin on the rectangular examining area (assuming that the two are similar rectangles).
Area of the cut tin sheet, 135 square cm
Area of uncovered examining area, 112-135=23 cm
Problem description does not give a way to relate the examining area to the rectangular cut sheet of tin. One can only assume and not really know that the examining area is the same dimensions as the UNCUT sheet of tin.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The "examining" area? Really now -- you should look at what you have written before you post your question.
From the context of the problem, it is clear that you mean the REMAINING area is 112cm^2....
You don't need algebra to solve this problem.
The difference between the length and width is 6cm; if the strip cut off is uniform, then the length and width of the remaining rectangular piece of tin will still differ by 6cm.
So look for a way to factor 112 as the product of two integers whose difference is 6.
Even without having any insight into the answer, a little trial and error should find the new dimensions to be 14cm by 8cm.
So the width and length have both been shorted by 1cm; since the uniform strip was cut off on all four sides, the width of the strip is 0.5cm.
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