Question 1124406
.
.
The problem assumes that the walkway has a uniform width.



1. &nbsp;&nbsp;<U>The easy way to solve it MENTALLY</U>


<pre>
The difference the length minus the width of the garden is  15 - 12 = 3 ft.


Since the walkway is of uniform width, the difference between the length and the width of the large rectangle
    must be the same 3 ft.


So we need to find a decomposition of the number 238 (238 sq.ft., the area) into the product of two numbers with 
   the difference of 3 between them.


As soon as you re-formulated the problem in this way, you can guess the answer MENTALLY and MOMENTARILY: 
    the numbers are 14 and 17.

    238 = 2*119 = 2*7*17 = 14*17.


<U>Answer</U>.  The dimensions of the large rectangle are 14 and 17 feet.

         The uniform width of the border is 1 ft.  ( = {{{(14-12)/2}}} = {{{(17-15)/2}}}. )
</pre>


2. &nbsp;&nbsp;<U>Formal algebra solution</U>


<pre>
Let x be the uniform walkway width.

Then the dimensions of the larger rectangle are (15+2x)  and  (12+2x) feet.


So the area of the large rectangle is

(15+2x)*(12+2x) = 238.


It is your equation to find the unknown x.


Simplify it; write as a quadratic equation in standard form and solve by using the quadratic formula or factoring.
</pre>

-------------------


If you want to see many other similar solved problems, look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Surface-area/Problems-on-the-area-of-a-rectangle-surrounded-by-a-strip.lesson>Problems on the area and the dimensions of a rectangle surrounded by a strip</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Surface-area/Cynthia-Besch-and-the-rug.lesson>Cynthia Besch wants to buy a rug for a room</A> 

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic 
"<U>Dimensions and the area of rectangles and circles and their elements</U>".


Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.