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problem I can't solve: trapezoid w/ bases 14m,16m inscribed in square

allegansveritatem

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Jan 10, 2018
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there is a problem in my algebra book I can't solve for the life of me. The book is: College Algebra, Robert Blitzer. The problem: A trapezoid with bases of 14m and 16m is drawn inside a square (there is a diagram in the book illustrating this problem with the sides of the trapezoid not touching the sides of the square) . The area inside the square but outside of the trapezoid is 675 square meters. What is the height of the trapezoid.

How is this problem solved. It seems to me that there is not enough information given. I can't even begin to solve this. There are two variables. How can this be set up so that it can be solved in terms of just one variable, namely the height of the trapezoid?
 
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stapel

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there is a problem in my algebra book I can't solve for the life of me. The book is: College Algebra, Robert Blitzer. The problem: A trapezoid with bases of 14m and 16m is drawn inside a square (there is a diagram in the book illustrating this problem with the sides of the trapezoid not touching the sides of the square) . The area inside the square but outside of the trapezoid is 675 square meters. What is the height of the trapezoid.

How is this problem solved. It seems to me that there is not enough information given. I can't even begin to solve this. There are two variables. How can this be set up so that it can be solved in terms of just one variable, namely the height of the trapezoid?
Please reply with the rest of the information, including whatever are the two variables you've been given, and a scan of (or a much more complete description of) the "diagram". When you reply, please let us know if you're familiar with formulas for area, etc, of trapezoids and squares. If you haven't learned some of the necessary background info, please specify the topics over which you first need lesson instruction. Thank you! ;)
 

allegansveritatem

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Jan 10, 2018
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240
h = height of trapezoid

area = h(14 + 16)/2 = 15h

c = side of square

c^2 - 15h = 675
h = (c^2 - 675) / 15

Did you get that far?
Yes, I tried something like this: x^2= 1/2h(14+16) + 675 but that still doesn't get me either x or h.
 

allegansveritatem

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Jan 10, 2018
Messages
240
Blitzer.JPG
Please reply with the rest of the information, including whatever are the two variables you've been given, and a scan of (or a much more complete description of) the "diagram". When you reply, please let us know if you're familiar with formulas for area, etc, of trapezoids and squares. If you haven't learned some of the necessary background info, please specify the topics over which you first need lesson instruction. Thank you! ;)
 

Dr.Peterson

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Nov 12, 2017
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Yes, I tried something like this: x^2= 1/2h(14+16) + 675 but that still doesn't get me either x or h.
Without additional information, I don't see how the problem could be solved. Taking x as the height and y as the side of the square (why did you use x for the latter?), we have as previously stated, y^2 = 15x + 675. This might be solvable if you were told, say, that x and y must be integers or have some particular relationship; but you weren't.

I have a Blitzer College Algebra book, but there are several; your figure 3.27 is not mine. What chapter is this in, and what topics might it relate to?
 

allegansveritatem

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Jan 10, 2018
Messages
240
Without additional information, I don't see how the problem could be solved. Taking x as the height and y as the side of the square (why did you use x for the latter?), we have as previously stated, y^2 = 15x + 675. This might be solvable if you were told, say, that x and y must be integers or have some particular relationship; but you weren't.

I have a Blitzer College Algebra book, but there are several; your figure 3.27 is not mine. What chapter is this in, and what topics might it relate to?
The edition I have was printed in 1995...seems to be the first edition. The page number the problem is on is 224. The section is 3.3 Geometry Problems which begins on page 207. Maybe you can't find the problem because you have a later edition from which this problem (being the result of a typo) was removed. It seems to be unsolvable as it stands. Maybe, as I suggest above, something was left out by mistake in the first edition. Subsequent editions simply omitted it altogether. No?
 

Dr.Peterson

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Nov 12, 2017
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The edition I have was printed in 1995...seems to be the first edition. The page number the problem is on is 224. The section is 3.3 Geometry Problems which begins on page 207. Maybe you can't find the problem because you have a later edition from which this problem (being the result of a typo) was removed. It seems to be unsolvable as it stands. Maybe, as I suggest above, something was left out by mistake in the first edition. Subsequent editions simply omitted it altogether. No?
You're probably right. The other possibility is that you failed to look at instructions for the set of problems, which might have directed you to merely decided whether each problem could be solved!

Otherwise, my only hope would be that, if I saw other problems around it, I might be able to guess what the problem was intended to be; but there wouldn't be much point in that.

I doubt I would find a 20 year old college textbook; it is not online or in my college library. The edition I have contains no section on geometry problems; the book has probably been completely rewritten due to changed expectations.
 
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