SOLUTION: Construction. A garden area is 30 ft long and 20 ft wide. a path of uniform width is set around the edge. If the remaining garden area is 400 ft^2 , what is the width of the path?

Question 119472: Construction. A garden area is 30 ft long and 20 ft wide. a path of uniform width is set around the edge. If the remaining garden area is 400 ft^2 , what is the width of the path?
So if I squared 20, 30, 400 And I get something like 30 ft, would I be terribly wrong?
Answer by ptaylor(1894) (Show Source):
You can put this solution on YOUR website!
I THINK YOU BEST APPROACH ON WORD PROBLEMS IS TO LAY THEM OUT IN AN ORDERLY FASHION IDENTIFYING WHAT NEEDS TO BE DETERMINED AS YOU GO. I HAVE TRIED TO DO THIS BELOW:
Area(A)=Length(l) times Width(w) or A=l*w
Let w=the uniform width of the path. Note that the path is inside the original garden

Note: draw the garden and path and the statement below will be obvious.
Area of garden after path is put in= (20-2w)*(30-2w) =600-100w+4w^2 and this we are told equals 400 ft^2. So:
600-100w+4w^2=400 subtract 400 from both sides
600-400-100w+4w^2=400-400 collect like terms
4w^2-100w+200=0 divide each term by 4
w^2-25w+50=0 quadratic in standard form. Solve using the quadratic formula:

ft----------------------too large-- gives a negative value for length and width--- not a correct answer
and

ft----ans
(30-2*2.2)(20-2*2.2)=400
(30-4.4)(20-4.4)=400
25.6*15.6=400
~~~400=400
Hope this helps---ptaylor