SOLUTION: One formula stating the relationship between length l and width w of a rectangle of "pleasing proportion" is {{{ l^2=w(l+w) }}}. How should a 4 foot by 8 foot sheet of plasterboard

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Question 669064: One formula stating the relationship between length l and width w of a rectangle of "pleasing proportion" is +l%5E2=w%28l%2Bw%29+. How should a 4 foot by 8 foot sheet of plasterboard be cut so that the result is a rectangle of “pleasing proportion” with a width of 4 feet?
I really don't even know where to start. Thanks! :-)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What they are saying is that you need to end
up with a piece of plasterboard that is
4 feet by +l+ feet, and you need the formula
+l%5E2+=+w%2A%28+l+%2B+w+%29+ to find +l+
------------
++w+=+4+
+l%5E2+=+4%2A%28+l+%2B+4+%29+
+l%5E2+=+4l+%2B+16+
+l%5E2+-+4l+=+16+
Complete the square
+l%5E2+-+4l+%2B+%28+%28-4%29%2F2+%29%5E2+=+%28+%28-4%29%2F2+%29%5E2+%2B+16+
+l%5E2+-+4l+%2B+4+=+4+%2B+16+
+%28+l+-+2+%29%5E2+=+%28+sqrt%2820%29+%29%5E2+
+i+-+2+=+sqrt%2820%29+
+l+=+2+%2B+2%2Asqrt%285%29+
+l+=+2+%2B+4.472+
+l+=+6.472+
The dimensions are 4' x 6.472'
check:
+l%5E2+=+4%2A%28+l+%2B+4+%29+
+41.887+=+4%2A10.472+
+41.887+=+41.888+
Looks close enough