Question 736089
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Multiplying the expressions for the measures of the sides of a rectangle gives you the area of the rectangle.  *[tex \LARGE x^2\ +\ 2x] is indeed the correct expression for the product you describe and had you provided a number that represents the area of the rectangle, it would be a simple matter to set your product of sides expression equal to the given area from which it is a fairly simple manipulation to construct a quadratic equation in standard form.  But lacking such a number representing the area, I can only show you in general what to do.  Let *[tex \LARGE A] represent the numerical value of the area of your rectangle.  Then:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 2x\ =\ A]


which can be converted to


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 2x\ -\ A\ =\ 0]


Substitute your area value when you find it and solve the quadratic.  By the way, such a quadratic will have two distinct roots and one of them will be negative.  Since a negative number is an absurd value for a measure of the length of a side of a rectangle, discard that root.  The positive root will be the width of your rectangle and the value *[tex \LARGE x\ +\ 2] will be the length.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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