SOLUTION: The dimensions of a rectangular garden are 5m x 8m. There is a path around the garden of uniform width that is the same area as the garden. What are the dimensions of the backyard?

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: The dimensions of a rectangular garden are 5m x 8m. There is a path around the garden of uniform width that is the same area as the garden. What are the dimensions of the backyard?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1140065: The dimensions of a rectangular garden are 5m x 8m. There is a path around the garden of uniform width that is the same area as the garden. What are the dimensions of the backyard? (DRAW PICTURE)
Found 3 solutions by KMST, ikleyn, MathTherapy:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The garden is a rectangle with area %285m%29%2A%288m%29=40m%5E2 .
A path of width x%2F2m around that garden would add xm to the length and xm to the width of that rectangle. The garden plus the path would form a larger rectangle with length 8%2Bx m and width 5%2Bxm . The area of that larger rectangle would be double the area of the garden: 2%2840m%5E2%29=80m%5E2 .
So %28x%2B8%29%2A%28x%2B5%29=80 .
x%5E2%2B13x%2B40=80
x%5E2%2B13x-40=0 or x%5E2%2B13x=40
That equation can be solved by completing the square, or applying the quadratic formula to find as solutions
x=%28-13+%2B-+sqrt%28329%29%29%2F2 .
As we were adding a length x%3E0 to the width and length of the garden,
the only applicable answer is
x=%28-13+%2B+sqrt%28329%29%29%2F2=sqrt%28329%29%2F2-6.5=about2.569 (making x%2F2=about1.286m.
Adding that to the garden's dimensions,
he width (in m) of garden plus path would be
5-6.5+%2B+sqrt%28329%29%2F2=sqrt%28329%29%2F2%7D-1.5=about7.57 ,
and the length (in m) of the garden plus path would be
8%2B+sqrt%28329%29%2F2-6.5=sqrt%28329%29%2F2%7D%2B1.5=about10.57 .


Is there anything else in that backyard? A pool? A patio? A chicken coop? A stream?
If the backyard is only the garden and the path of uniform width around it, with the same area as the garden, then the backyard's dimensions are as stated above

Answer by ikleyn(52785) About Me  (Show Source):
You can put this solution on YOUR website!
.

I'd say that the question is not relevant to the given part, as well as the given part is not relevant to the question.


My impression is that two different parts of two different problems are mixed in this post.


Or, possible, the person who invented this text, forgot the beginning, wheh formulated his question.


/\/\/\/\/\/\/\/

My general point is that the visitors, who came to this forum, have the need in general education even more than in Math.



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The dimensions of a rectangular garden are 5m x 8m. There is a path around the garden of uniform width that is the same area as the garden. What are the dimensions of the backyard? (DRAW PICTURE)
Let width of path be W

Correct equation: (5 + 2W)(8 + 2W) = 80 =====> matrix%281%2C3%2C+2W%5E2+%2B+13W+-+20%2C+%22=%22%2C+0%29

Solve that for W, the width of the UNIFORM path. You should get a value of: highlight_green%28matrix%281%2C2%2C+1.28459%2C+m%29%29

Add this to 5 and to 8 to get the dimensions of the backyard, considering that it only contains the garden and the UNIFORM path around the garden.