SOLUTION: A garden is 15 ft by 13 ft. You are building a walkway around this garden that is of uniform width. The area of the garden and walkway together is 30 less than twice the area of

Algebra.Com
Question 1053331: A garden is 15 ft by 13 ft. You are building a walkway around this garden that is of
uniform width. The area of the garden and walkway together is 30 less than twice the
area of the garden. Find the width of the walkway.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
The type of problem is a slight variation of this kind:

rectangular outside-border - video
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
A garden is 15 ft by 13 ft. You are building a walkway around this garden that is of
uniform width. The area of the garden and walkway together is 30 less than twice the
area of the garden. Find the width of the walkway.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let "w" be the width of the walkway. 
Then the dimensions of the large rectangle are 15+2w and 13+2w.
The area of the large rectangle is the product (15+2w)*(13+2w).

The condition says

(15+2w)*(13+2w) = 2*15*13 - 30.

You need to solve this equation for w. Simplify:

15*13 + 30w + 26w + 4w^2 = 2*15*13 - 30,

4w^2 + 56w = 165,

4w^2 + 56w - 165 = 0.

Use the quadratic formula

 =  = .

 =  =  = 2.5 ft.   (Ignore the negative root).

Answer. 2.5 ft

For more similar solved problems see the lesson
    - Problems on the area and the dimensions of a rectangle surrounded by a strip
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 lesson is the part of this online textbook under the topic
"Dimensions and the area of rectangles and circles and their elements ".


RELATED QUESTIONS

Help! Don't know how to put story problem into quadratic formula: A rectangular garden (answered by MathLover1)
A rectangular garden is 30 ft by 40 ft. Part of the garden is removed in order to install (answered by ankor@dixie-net.com)
a rectangular garden is 49 ft and 35 ft wide. the garden is bordered by a rectangular... (answered by mananth)
A rectangular garden which is 12ft by 16ft is surrounding by a walkway which is a uniform (answered by Stitch)
I've racked my brain for hours & I still don't know where to begin on this problem: A... (answered by jim_thompson5910)
A vacant lot is being converted into a community garden. The garden and the walkway... (answered by ikleyn)
Construction. A garden area is 30 ft long and 20 ft wide. A path of uniform width is set... (answered by ankor@dixie-net.com)
A rectangular garden is to be surrounded by a walkway of width. The garden's dimensions... (answered by ankor@dixie-net.com)
A vacant lot is being converted into a community garden. The garden and the walkway... (answered by josmiceli)