Question 211852
A rectangular room has an area of 665 square feet. Its length is three less than twice its width. what are the dimensions of the room?


Step 1.  Let l = 2w-3  length of rectangle and let w be the width


Step 2.  Let A = 655 square feet be the Area = (length)(width)


{{{A=655=(2w-3)w}}}


{{{655=2w^2-3w}}}


Step 3.  Subtract 655 to both sides of equation to get 0 by left side


{{{655-655=2w^2-3w-655}}}


{{{0=2w^2-3w-655}}}


Step 4.  Now we have a quadratic equation so we can use the quadratic formula given as 


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


where a=2, b=-3 and c=-655.

The following steps solve the quadratic equation:


*[invoke quadratic "w", 2, -3, -655 ]


Step 5.  Choose the positive number for a positive length.  In this case, the width is 18.86 ft and length is 2w+3 or 2(18.86)-3 or 34.72 ft.


Step 6.  Answer is 18.86 ft for the width and 34.72 for the length.  Multiply these two numbers to get an area of 655 square feet.


Hope the above steps were helpful.  Good luck in your homework and studies!  


Respectfully
Dr J


Hope you understood and followed the steps. Good luck in your studies. Dr J 


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