SOLUTION: A gardener has 46 ft of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it. If the length of the garden is twice its width what will b

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Question 213396This question is from textbook
: A gardener has 46 ft of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it.
If the length of the garden is twice its width what will be the dimensions of the garden?This question is from textbook

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
A gardener has 46 ft of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it. If the length of the garden is twice its width what will be the dimensions of the garden?

Step 1. Let L=2w be the length of garden and let w garden

Step 2. Let L+2 and w+2 include the border
Step 3. Let P = 46 ft be the perimeter. Perimeter means adding the 4 sides of a rectangle. So,

P=L%2B2%2BL%2B2%2Bw%2B2%2Bw%2B2=2L%2B2w%2B8=2%282w%29%2B2w%2B8=6w%2B8

P=46=6w%2B8

Step 3. Subtract 8 from both sides of equation

46-8=6w%2B8-8

38=6w

Step 4. Divide 6 to both sides of equation to get w by itself


38%2F6=6w%2F6

w=19%2F3

Step 5. w = 19/3 is the width of the rectangle and length L is 38/3 since L=2w%29. With the border w+2=25/3 and 2w+2=44/3

Check P=6w+8= 6*(19/3)+8= 46 So w = 25/3 ft and L=44/3 is the solution.

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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