SOLUTION: This is a factoring word problem when you have to use the principle of zero. The problem says A garden that is 4 meters wide and 6 meters long is to have a uniform border such that

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: This is a factoring word problem when you have to use the principle of zero. The problem says A garden that is 4 meters wide and 6 meters long is to have a uniform border such that      Log On


   

Question 120170: This is a factoring word problem when you have to use the principle of zero. The problem says A garden that is 4 meters wide and 6 meters long is to have a uniform border such that the area of the border is the same as the area of the garden. Find the width of the border. Could you please help me?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First let's draw a picture. We can see that the length of the large rectangle is 6%2B2x and the width of the large rectangle is 4%2B2x since we are adding 2x to both the length and the width. note: the inner blue rectangle is the garden



From the drawing, we can see that the area of the small rectangle is: A=L%2AW=6%2A4=24


Also, from the drawing, the area of larger rectangle is:

A=%286%2B2x%29%284%2B2x%29


Now since we only want the area of the walkway, just subtract the area of the garden from the larger rectangle's area to get


A=%286%2B2x%29%284%2B2x%29-24


Now since the area of the walkway is the same as the garden, this means A=24

24=%286%2B2x%29%284%2B2x%29-24 Plug in A=24



24=4x%5E2%2B20x%2B24-24 Foil


0=4x%5E2%2B20x%2B24-24-24 Subtract 24 from both sides


0=4x%5E2%2B20x-24 Combine like terms



4%28x%2B6%29%28x-1%29=0 Factor the right side



Now set each factor equal to zero:
x%2B6=0 or x-1=0

x=-6 or x=1 Now solve for x in each case


So our possible answers are
x=-6 or x=1


However, since a negative length doesn't make sense, our only solution is x=1


So the walkway's width is 1 meter