Working With A Rectangular Garden

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nycmathguy
Homework Statement
1. Draw a diagram representing the problem.
2. Write equation representing the perimeter.
Relevant Equations
P = 2L + 2W
The length and width of a rectangular garden are 15 meters and 10 meters, respectively. A walkway of width x surrounds the garden.

(a) Draw a diagram that gives a visual representation of the problem.

(b) Write the equation for the perimeter y of the walkway in terms of x.

For (a), see attachment.

For (b):

y = 2L + 2W

y = 2(x + 15) + 2(x + 10)

y = 2x + 30 + 2x + 20

y = 4x + 50

Is any of this right?
 
Attachments
  • Hand-drawn red diagram of a rectangular garden with a larger outer rectangle around it, the gap between them labelled x on the left and right sides, the inner rectangle labelled 10 and the bottom edge labelled 15.
    Screenshot_20210619-182339_Drawing Pad.jpg
    18.1 KB · Views: 227
nycmathguy said:
Homework Statement:: 1. Draw a diagram representing the problem.
2. Write equation representing the perimeter.
Relevant Equations:: P = 2L + 2W

y = 2(x + 15) + 2(x + 10)
y=2(2x+15)+2(2x+10)
 
Attachments
  • Hand-drawn diagram of a rectangle inside a larger rectangle, with a red outer border and a blue inner rectangle; the inner rectangle's width is labelled 10 and its bottom edge 15, and the sides of the outer rectangle are labelled X.
    garden walkway width x.jpg
    11.4 KB · Views: 223
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anuttarasammyak said:
y=2(2x+15)+2(2x+10)
I was right the first time but doubted my work.
 
nycmathguy said:
A walkway of width x surrounds the garden.
(a) Draw a diagram that gives a visual representation of the problem.

nycmathguy said:
I was right the first time but doubted my work.
Your diagram, which is part a, is incorrect. The work for part b, but it doesn't align with your drawing. You have x being the length of the short side of the outer rectangle. Per the problem statement, x is the width of the walkway.
 
I think we should discriminate between the outer and the inner perimeter of the walkway.
The outer perimeter of the walkway is 2(2x+15)+2(2x+10).
The inner perimeter of the walkway is equal to the perimeter of the garden, that is 2*15+2*10.
 
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Mark44 said:
Your diagram, which is part a, is incorrect. The work for part b, but it doesn't align with your drawing. You have x being the length of the short side of the outer rectangle. Per the problem statement, x is the width of the walkway.
Can you draw the right figure for me?
 
nycmathguy said:
Can you draw the right figure for me?
Come on... you can do it. The garden is 15 by 10, and there is a walkway around the garden that is x feet wide.
 
Mark44 said:
Come on... you can do it. The garden is 15 by 10, and there is a walkway around the garden that is x feet wide.
See attachment.
 
Attachments
  • Hand-drawn red diagram of a rectangle inside a larger rectangle, with a border of width x; inner rectangle labelled 10 on the left side and 15 on the bottom, outer sides labelled x and 15 along the bottom edge.
    Screenshot_20210621-164120_Drawing Pad.jpg
    20.4 KB · Views: 191