SOLUTION: A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width. The combined area of the lawn and flower bed is 165mē. What is the width of the flower bed?

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Question 325298: A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width. The combined area of the lawn and flower bed is 165mē. What is the width of the flower bed?
Let x be the width of the flowerbed
(8+2x)(4+2x)=165
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given equation.


FOIL


Subtract 165 from both sides.


Combine like terms.


Notice that the quadratic is in the form of where , , and


Let's use the quadratic formula to solve for "x":


Start with the quadratic formula


Plug in , , and


Square to get .


Multiply to get


Rewrite as


Add to to get


Multiply and to get .


Take the square root of to get .


or Break up the expression.


or Combine like terms.


or Simplify.


So the solutions are or


However, 'x' is a length. So we'll ignore the negative answer.


So the width of the flower bed is which is 3.5 meters.
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