Question 1170832
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<pre>

    (28-2x)*(32-2x) = 192    (the area of the picture, in square inches)


    (14-x)*(16-x) = 48


    x^2 - 30x + 14*16 - 48 = 0


    x^2 - 30x + 176 = 0.


Factor it                 <<<---===  re-edited starting from this point


    (x-8)*(x-22) = 0.


The roots are  x= 8  and x= 22.


Due to the problem's meaning, only the root  x= 8 is the possible width of the frame (22 is not).


Thus the dimensions of the picture are  28-2*8 = 12 inches  and  32 - 2*8 = 16 inches.    <U>ANSWER</U>
</pre>

Solved.


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To see many other similar solved problems, &nbsp;look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Surface-area/Problems-on-the-area-of-a-rectangle-surrounded-by-a-strip.lesson>Problems on the area and the dimensions of a rectangle surrounded by a strip</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Surface-area/Cynthia-Besch-and-the-rug.lesson>Cynthia Besch wants to buy a rug for a room</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Surface-area/Circular-pool-and-a-walkway-around.lesson>Problems on a circular pool and a walkway around it</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Surface-area/OVERVIEW--of-lessons-on-dimensions-and-the-area-of-rectangles-and-circles.lesson>OVERVIEW of lessons on dimensions and the area of rectangles and circles and their elements</A>

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic 
"<U>Dimensions and the area of rectangles and circles and their elements</U>".


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.