A rectangular flower bed 3m wide, and 5m long.....?

A rectangluar flower bed, 3m wide and 5m long is surrounded by a sidewalk of uniform width. If the area of the sidewalk is 48m*2, what are the outside dimensions of the sidewalk?








i know the answer, i just don't know how to show my work for it

A rectangular flower bed 3m wide, and 5m long.....?
Let x be the width of the sidewalk on each side. Adding x twice to both dimensions, the final outside dimensions will be:


2x + 3 (wide) by 2x + 5 (long).





+------------------+


| xxxxxxxxxx |


| x |. 3 * 5 .| x | (new width = 3 + x + x)


| xxxxxxxxxx |


+------------------+


.. (new length = 5 + x + x)





We are told the sidewalk area is 48m², but this doesn't include the inside flower bed. Add the flower bed area (3m x 5m = 15m²) and you get a total of 63m².





Using the dimensions of 2x + 3 wide by 2x + 5 long you should get an area of 63. In equation form:





(2x + 3)(2x + 5) = 63





Expand out with FOIL:


4x² + 10x + 6x + 15 = 63


4x² + 16x + 15 = 63





Subtract 63 from both sides:


4x² + 16x - 48 = 0





I'd divide everything by 4 to simplify things:


x² + 4x - 12 = 0





You can easily factor this as:


(x + 6)(x - 2) = 0





x = -6 or x = 2





Since you can't have the sidewalk with a negative width the sidewalk must be 2m wide on each side. Adding twice this to each dimension you have:


2x + 3 = 7m wide


2x + 5 = 9m long





Answer:


The outside dimensions are 7m x 9m
Reply:Find the area of the bed.





A=LW


A=5(3)


A=15 m^2 for bed





Then, subtract the area of sidewalk by the area of bed.





48-15=33





Find the factors of the sidewalk....





ANSWER = 11 meters long and 3 meters wide.