Question 1143612
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<pre>
Let y be the value exactly half-way between the length and the width.


Then the length = y+7.  while the width = y-7.


The area is the product of length and width, i.e. (y+7)*(y-7) = {{{y^2 - 49}}}.


Then the area equation is 


    {{{y^2-49}}} = 400,


which implies


    {{{y^2}}} = 400 + 49 = 449,

    y = {{{sqrt(449)}}}.


Thus the length = {{{sqrt(449)}}} + 7 = 28.190 (approximately, with 3 right decimal places).    <U>ANSWER</U>

and  the width  =  {{{sqrt(449)}}} - 7 = 14.190 (approximately, with 3 right decimal places).    <U>ANSWER</U>


<U>CHECK</U>.  The product of  {{{sqrt(449)}}} + 7  and  {{{sqrt(449)}}} - 7  is  400 = 449-49,  and the difference is 14, obviously.
</pre>

Solved.


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Surely, this method is the same as to solve the problem using the quadratic formula, and it gives the same answer.


Its advantage is in that it is not so boring . . . 



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To see many other problems solved by the similar method, look into the lessons

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