SOLUTION: A rectangular parking lot has dimensions 16 metres by 40 metres. The total area of the parking lot is increased by 512 square metres by paving an extra strip of uniform width aroun

Discussion





The key thing to remember in this problem is that the width of the added strip

is uniform, meaning it is the same width all the way around, and that the

overall length and overall width of the parking lot has been increased by 2

times this width.







Solution











Let x = the width of the uniform strip.  Then the new width of the parking lot 

is  meters and the new length of the parking lot is  meters.





So the overall area of the new larger parking lot is 





But this area is  larger than the area of the old parking lot which

was .





Therefore we can write: 





Multiply the binomials and collect like terms:











Divide by 4 and put in standard form:







Factor:















So  or 





Since we are looking for a positive length, we can exclude the negative root.

The width of the strip around the old parking lot is 4 metres.







Check Answer





 Checks.