SOLUTION: A path, 3 meters wide, runs around the outside edge of a rectangular court. The court is half as long again as it is wide. The area of the path is 1596 square meters. What are t

Question 1091595: A path, 3 meters wide, runs around the outside edge of a rectangular court.
The court is half as long again as it is wide.
The area of the path is 1596 square meters.
What are the dimensions of the court?
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
The court is x m wide and (3/2)x m long.
The court plus the path is (x+6) m wide and (3/2)x+6 m long
The area of the court is 1.5 x^2 m^2.
The area of the whole thing is 1.5 x^2+15x+36 m^2
The area of the path is their difference, which is 15x+36=1596 m
15x=1560 m
x=104 m wide
(3/2)x=156 m long
area of the court is 16,224 m^2
with the path, the dimensions are 110 x 162=17,820, and that difference is the area of the path, or 1596 m^2.

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
For many other similar problems and their detailed solutions, see the lessons
    - Problems on the area and the dimensions of a rectangle
    - Problems on the area and the dimensions of a rectangle surrounded by a strip
    - Problems on a circular pool and a walkway around it
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Dimensions and the area of rectangles and circles and their elements".

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