Question 780474
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So you don't know the width of the border.  That makes the width of the border a good candidate to be *[tex \LARGE x], right?  Then the width of the area in the center that is supposed to measure 96 square yards has to be the 10 yards that is the width of the porch minus *[tex \LARGE x] yards <b>on each side</b>, so *[tex \LARGE 10\ -\ 2x].  Likewise, the length of the center part has to be *[tex \LARGE 20\ -\ 2x].  The area of a rectangle is the length times the width, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ (10\ -\ 2x)(20\ -\ 2x)\ =\ 96]


Multiply the two binomials, collect all terms in the LHS so that the LHS is equal to zero, and then solve by any convenient means.  Given your lesson for today on the quadratic formula, the need for such is a reasonably good guess.  However, once you calculate the discriminant, you should see that the radicand is a perfect square.  Hence the quadratic is indeed factorable.  You will get two positive roots of this equation but one of them is absurd, so discard it. 


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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