Question 209727
Area of a rectangle is 243 m^2. The height is nine less than 4 times the base. What is the perimeter?


Step 1.  Let x be the base and 4x-9 be the height


Step 2.  Perimeter P means adding up the four sides of a rectangle.


Step 3.  Then {{{P=x+x+4x-9+4x-9=10x-9}}}


Step 4.  Area=x*(4x-9)=243  or 4x^2-9x-243=0 or a quadratic equation.


Step 5.  We can use the quadratic formula given as 


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


where a=4, b=-9 and c=-243


*[invoke quadratic "x", 4, -9, -243]


Select the positive number x=9.



Step 6.  Then {{{P=x+x+4x-9+4x-9=10x-9=10*9-9=81}}}


Step 7.  ANSWER:  The perimeter is 81.



I just found this problem on 18 Sep 09, but I hope the above steps were helpful for review.  Sorry about the late response.


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And good luck in your studies!


Respectfully,
Dr J