Working With A Rectangular Garden

[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?

 

[anuttarasammyak]

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)

 

[nycmathguy]

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

I was right the first time but doubted my work.

 

[Mark44]

A walkway of width x surrounds the garden.
(a) Draw a diagram that gives a visual representation of the problem.

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.

 

[Delta2]

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.

 

[nycmathguy]

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?

 

[Mark44]

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.

 

[nycmathguy]

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.