SOLUTION: A small rectangular playground that is 10ft by 14ft is going to have a grass border of uniform width on all sides. If the area of the grass is 145 sq ft how wide is the border?
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Question 315122: A small rectangular playground that is 10ft by 14ft is going to have a grass border of uniform width on all sides. If the area of the grass is 145 sq ft how wide is the border? Answer by solver91311(24713) (Show Source):
If the inner rectangle (the playground part) is 10 by 14 and we let represent the width of the grass border, then the overall size of the rectangle is by because the walkway is on both sides and on the top and bottom, so two widths of the walkway in each direction.
The area of just the playground is
The area of just the grass border is given as
So the total area must be
But since the overall dimensions are by , the total area must also be represented by:
Which we have determined is equal to 285, so:
Hence
Fortunately for those of us who enjoy nice neat rational number answers, this little quadratic factors rather neatly:
Which means that
or
The idea of a grass border that is -14.5 feet wide is simply ludicrous, so discard that root. The correct answer is 2.5 feet.
