Question 1193348
.
A soccer field has a perimeter of 288 meters and an area of 4,860 square meters. 
What are the dimensions of the field?
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<pre>
Let x be the length, in meters;  y be the width.


Then x + y = 288/2 = 144  (half of the perimeter).


Consider the arithmetic mean of x and y, which is  {{{(x+y)/2}}} = {{{144/2}}} = 72.


Then, obviously,  x = 72+a, y = 72-a  for some value of "a"  (x and y are equally remoted from the arithmetic mean).


Therefore, the area of the field is

    area = x*y = (72+a)*(72-a) = {{{72^2}}} - {{{a^2}}} = 5184 - {{{a^2}}}.


So, the area equation is  

    5184 - {{{a^2}}} = 4860.


From this equation,  find  "a"

    {{{a^2}}} = 5184 - 4860

    {{{a^2}}} =     324

    a   =  {{{sqrt(324)}}} = 18.


Thus the dimensions of the field are  x = 72+18 = 90 meters  and  y = 72-18 = 54 meters.


<U>ANSWER</U>.  The dimensions of the field are  90 meters by 54 meters.
</pre>

Solved.


The method showed in my post is non-standard method, &nbsp;which is rarely used in traditional school education.


Its advantage is in that in many cases it allows to get the answer without long calculations - 

practically &nbsp;MENTALLY, &nbsp;as you see in the given case.


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


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

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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Surface-area/Three-methods-to-find-the-dimensions-of-a-rectangle-when-the-givens-are-its-perimeter-and-the-area.lesson>Three methods to find the dimensions of a rectangle when its perimeter and the area are given</A>

in this site.


The first reference is the standard method; &nbsp;the second reference teaches non-standard methods.


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.