Question 1178962
.
The area of a {{{highlight(rectangular)}}} garden is 972 square feet, and the length of its diagonal is 45 feet. 
Find the dimensions of the garden.
~~~~~~~~~~~~~~~~~



            The solution by @Mananth is irrelevant and has nothing in common with the problem.


            For your safety,  simply  IGNORE  HIS  (or her)  POST.


            I came to bring the correct solution.


            Notice how I edited the condition in order for the problem would make sense.



<pre>
Let x be the larger dimension of the rectangle, 

and let y be its smaller dimension.


Then we have these two equations from the condition


    xy = 972            (1)

    {{{sqrt(x^2 + y^2)}}} = 45.    (2)


From equations (1) and (2), you get


    x^2 + 2xy + y^2 = {{{45^2}}} + 2*972 = 3969 = {{{63^2}}}

    x^2 - 2xy + y^2 = {{{45^2}}} - 2*972 =   81 = {{{9^2}}}.



It can be simplified to

    x + y = 63

    x - y =  9


It implies  2x = 63+ 9 = 72;  x = 36;  y = 27.


<U>ANSWER</U>.  The dimensions of the rectangle are 36 feet and  27 feet.
</pre>


Solved (correctly).