Question 212033
A rectangular piece of carpet has a length that is 5 yards shorter than twice its width.  The area of the carpet is 88 square yards. Find the width only.


Step 1.  Let x be the width of carpet.


Step 2.  Let x-5 be the length of carpet


Step 3.  Area = width * length


{{{x(x-5)=88}}}


{{{x^2-5x=88}}}



Subtract 88 from both sides of equation to get a quadratic equation


{{{x^2-5x-88=88-88=0}}}


Step 4.  This is a quadratic equation.  So we can use the formula  


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


where a=1, b=-5 and c=-88.



Now follow the steps below to solve a quadratic equation and select the positive number since we have positive lengths.


*[invoke quadratic "x", 1, -5, -88 ]



Step 5.  So width is 12.21 and length is 7.21 since length = x-5.


Hope this helps!  Dr J



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