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.