SOLUTION: I have tried this problem and cannot seem to get an answer for it! Please help me!!! Here it is: A garden with an area of 105 square meters is surrounded by a sidewalk of unif

Algebra ->  Rate-of-work-word-problems -> SOLUTION: I have tried this problem and cannot seem to get an answer for it! Please help me!!! Here it is: A garden with an area of 105 square meters is surrounded by a sidewalk of unif      Log On


   

Question 83999: I have tried this problem and cannot seem to get an answer for it! Please help me!!! Here it is:
A garden with an area of 105 square meters is surrounded by a sidewalk of uniform width. The sidewalk and garden together are 19 meters long and 11 meters wide. How wide is the sidewalk?
A: 1 meter B: 2 meters C: 1.5 meters D: 0.5 meters
I did:
19 x 11 = 209
209-105 = 104
... I don't know what to do from there!
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
you're kind of on the right track ... let x be the width of the sidewalk

the dimensions of the garden are the overall dimensions minus twice the width of the sidewalk

area=(length)(width) ... 105=(19-2x)(11-2x) ... 105=209-60x+4x^2 ... 0=104-60x+4x^2

x^2-15x+26=0 ... (x-13)(x-2)=0 ... x=13, x=2 ... the 13 is not a realistic solution (overall width is only 11)