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As part of a landscaping project, you put in a flower bed measuring 10 feet by 50 feet. To finish off the project, you are putting in a uniform border of pine bark around the outside of the rectangular garden. You have enough pine bark to cover 396 square feet. How wide should the border be?

User FindIt
by
8.5k points

1 Answer

2 votes

Answer:

Let's denote the width of the border as

x feet. Since the border goes around the outside of the flower bed, it would increase both the length and the width of the flower bed by

2

2x feet.

The new dimensions of the flower bed with the border will be:

Length:

10

+

2

10+2x feet

Width:

50

+

2

50+2x feet

The area of the flower bed with the border is given by the product of its length and width:

(

10

+

2

)

(

50

+

2

)

(10+2x)(50+2x)

According to the problem, the area covered by the pine bark is 396 square feet. So, we can set up the equation:

(

10

+

2

)

(

50

+

2

)

=

396

(10+2x)(50+2x)=396

Now, we can solve for

x:

500

+

20

+

2

2

=

396

500+20x+2x

2

=396

2

2

+

20

+

500

396

=

0

2x

2

+20x+500−396=0

2

2

+

20

+

104

=

0

2x

2

+20x+104=0

Divide the equation by 2:

2

+

10

+

52

=

0

x

2

+10x+52=0

Unfortunately, this quadratic equation doesn't have real solutions, as its discriminant (

2

4

b

2

−4ac) is negative. This indicates that the problem might not have a valid solution or there might be a mistake in the problem statement.

Explanation:

User Clay Smith
by
8.0k points