How do I solve 4800 = (2L-100)L

Question

Need help solving a word problem: The area of a rectangle is 4,800 square units. The width is 100 less than 2 times the length. What are the length and width of the rectangle?

Answer 1

Hi Sandy,

 

If you distribute the L into the parentheses, then manipulate your expression so that you have nothing on one side:

 

     0 = something you'll need to work out

 

Then you can use the quadratic equation to solve for possible values for L.

 

Best of luck! :)

Answer 2

4800 = (2L-100)L

 

So far, so good.  Now, distribute the L:

  4800 = 2L² - 100L

 

Then, put values on one side of the equation:

  2L² - 100L -4800 = 0

 

It is easier to factor (or use the quadratic formula) if we first divide by 2:

  L² - 50L - 2400 = 0

  (L - 80)(L + 30) = 0             [check it using F-O-I-L)

 

That means that either:

   L-80 = 0   or  L+30 = 0   or both       [Multiplication Property of Zero]

  L = 80       or  L = -30     or both

             But L=-30 doesn't make sense

 

L = 80

W = 2(80)-100 = 60

 

Check (very important):

L = 80

W = 2(80)-100 = 60

Area = LW = 80*60 = 4800