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?
Algebra.Com
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): You can put this solution on YOUR website!
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:
\left(14\ +\ 2x\right)\ =\ 4x^2\ +\ 48x\ +\ 140)
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:
\left(2x\ +\ 29\right)\ =\ 0)
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.
Check
\ =\ 15)
\ =\ 19)
Answer checks
John
RELATED QUESTIONS
A small rectangular playground that is 10ft by 14ft is going to have a grass border of a... (answered by ankor@dixie-net.com)
A small rectangular playground that is 10 feet by 14 feet is going to have a grass border (answered by checkley77)
A small rectangular playground that is 10feet by 14feet is going to have a grass border... (answered by checkley77)
A small rectangular playground that is 10 feet by 14 feet is going to have a grass border (answered by mananth)
A landscaper who just completed a rectangular flower garden measuring 6ft by 10ft orders... (answered by FrankM)
A rectangular flower bed with width 12 feet and length 15 feet is going to have a walkway (answered by CharlesG2)
A rectangular flower bed with the width 12 ft. and length 15 ft. is going to have a... (answered by nyc_function)
A rectangular flower bed with the width 12 ft. and length 15 ft. is going to have a... (answered by nyc_function)
A landscaper, who just completed a rectangular flower garden measuring 6 feet by 10... (answered by ikleyn)