9. The Cunard REcreation Center plans to build a 40 foot by 60 foot swimming poo
ID: 3100707 • Letter: 9
Question
9. The Cunard REcreation Center plans to build a 40 foot by 60 foot swimming pool.The pool must be surrounded by a concrete sidewalk of uniform width. What are the possible widths if the center wants the entire pool and sidewalk to be at least 3000 square feet?
* Please only answer this if you are 100% sure you know how. I need this right.
Thanks, and I appreciate all of yalls help..Anonymous...
Explanation / Answer
x=40+2z y=60+2z where z is the width of the uniform sidewalk: 3000=(40+2z)(60+2z) 3000=2400+200z+4z^2 600=200z+4z^2 z^2+50z-150=0 Using the quadratic formula, we have a=1 b=50 c=-150 [-b (+/) sqrt(b^2-4ac)]/2a =2.8388ft or -52.8388 ft Since we cannot have a negative width, we find -52.8388ft to be extraneous. Therefore the only answer left (and the width of the path) is 2.8388ft. If we want to solve for the widths of the entire Swimming Pool and path width, we must solve the original two equations. x=40+2z--> x= 45.6776ft y=60+2z--> y= 65.6776ft These are the MINIMUM widths of the Center to provide at least 3000 square feet.
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