Question 1207920
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A garden 7 m by 12 m will be expanded by planting a border of flowers. 
The border will be of the same width around the entire garden and has an area of 92 {{{highlight(cross(im))}}} <U>square meters</U>.
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The question absents in this post, &nbsp;which is inaccuracy 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and disrespect to tutors, &nbsp;both in the same time.



<pre>
The garden is a rectangle 7 m by 12 m. Its area is 7*12 = 84 m^2.

Let w be the uniform width of the border of flowers around the garden.


The extended garden is a rectangle of dimensions (7+2x) by (12+2x) meters.
The area of the extended garden is (7+2x)*(12+2x) m^2.


The difference of these two areas is the area of the border around the garden.


So, we write this equation

    (7+2x)*(12+2x) - 84 = 92  square meters.    (1)


At this point, the setup is complete. 
Now our goal is to find x from this equation.    
Simplify it

    84 + 24x + 14x + 4x^2 - 84 = 92.

    4x^2 + 38x - 92 = 0,

    2x^2 + 19x - 46 = 0.


Use the quadratic formula

    {{{x[1,2]}}} = {{{(-19 +- sqrt(19^2 - 4*2*(-46)))/(2*2)}}} = {{{(-19 +- sqrt(729))/4}}} = {{{(-19 +- 27)/4}}}.


One root is positive, the other root is negative.

Naturally, we discard the negative root and accept the positive root

    x = {{{(-19 + 27)/4}}} = {{{8/4}}} = 2 meters.


<U>ANSWER</U>.  The uniform width of the border around the garden is 2 meters.


<U>CHECK</U>.    We check if equation (1) is correct.

          Its left side is (7+2*2)*(12+2*2) - 84 = use your calculator = 92 m^2,  

                                                   precisely as the given area of the border.
</pre>

Solved.


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