SOLUTION: An engineer wants to surround a rectangular a pool with dimension 10m by 20m with a stone border of uniform width. there are enough stones to cover 64 square meters . how wode shou

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Question 1096574: An engineer wants to surround a rectangular a pool with dimension 10m by 20m with a stone border of uniform width. there are enough stones to cover 64 square meters . how wode should the border be?
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
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.


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For many other similar solved problems see the lesson
    - Problems on the area and the dimensions of a rectangle surrounded by a strip
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 lesson is the part of this online textbook under the topic
"Dimensions and the area of rectangles and circles and their elements".



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Engineers don't do pool borders.