SOLUTION: A rectangular garden of length 28 ft and width 17 ft is surrounded by a path of uniform width. If the area of the walkway is 144 ft2, what is its width?

Algebra ->  Rectangles -> SOLUTION: A rectangular garden of length 28 ft and width 17 ft is surrounded by a path of uniform width. If the area of the walkway is 144 ft2, what is its width?       Log On


   

Question 1050788: A rectangular garden of length 28 ft and width 17 ft is surrounded by a path of uniform width. If the area of the walkway is 144 ft2, what is its width?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
A rectangular garden of length 28 ft and width 17 ft is surrounded by a path of uniform width.
If the area of the walkway is 144 ft2, what is its width?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 


The larger rectangle has the dimensions (28+2x) and (17+2x), where x is the uniform width of the walkway, in feet.

The smaller rectangle (the garden) has the area of 28*17 square feet.

You are given the difference

(28+2x)*(17+2x) - 28*17 = 144.

Simplify this equation 

28%2A17+%2B+56x+%2B+34x+%2B+4x%5E2 - 28*17 = 144,

4x%5E2+%2B+90x = 144,

4x%5E2+%2B+90x+-+144 = 0.

Apply the quadratic formula

x%5B1%2C2%5D = %28-90+%2B-+sqrt%2890%5E2-4%2A4%2A%28-144%29%29%29%2F%282%2A4%29 = %28-90+%2B-+102%29%2F8.

Ignore the negative root. Then you have an unique solution  x = 12%2F8 =  1 1%2F2 ft = 1.5 ft.

Answer.  The walkway width is 1.5 ft.

For more similar solved problems see the lessons
    - 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 parts of this textbook in the chapter "Dimensions and the area of rectangles and circles and their elements".