Question 1096574
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<pre>
Let w be the uniform width of the stone border.


Then the exterior dimensions of the larger rectangle are (10+2w) meters by (20+2w) meters, 
and the area of the larger rectangle is the product  (10+2w)*(20+2w) square meters.


Hence, the area of the border itself is  (10+2w)*(20+2w) - 10*20,  and it is equal exactly to  64 square meters.


It gives you an equation for w:

(10+2w)*(20+2w) - 10*20 = 64,

40w + 20w + 4w^2 = 64,

4w^2 + 60w - 64 = 0,

w^2 + 15w - 16 = 0,

(w+16)*(w-1) = 0  ====>   the only positive root  w= 1 gives you the answer to the problem's question.
</pre>


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For many other similar solved problems see the lesson

&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>

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>".