Area of a 5-by-3 pond and a y-m-wide pathway around the pond

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njbeep

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Aug 15, 2016
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Hi there, the question and my working out is as follows:

A rectangular pond has dimensions 5 m by 3 m. A pathway around the edge of the pond is y m wide on each side.
(a) Find the area of the pond.
(b) Find the area of the pond and the pathways.
(c) Find the area of the pathways.


A of pond = 5*3 = 15 m^2

Now i start to get a little unstuck, i think (b) should look something like this:

(3+2y)(5+2y) + 15

I am entirely uncertain what should happen with (c) and i would appreciate greatly an explanation.
Thank you in advance.
 
njbeep said:
A rectangular pond has dimensions 5 m by 3 m. A pathway around the edge of the pond is y m wide on each side.
(a) Find the area of the pond.
(b) Find the area of the pond and the pathways.
(c) Find the area of the pathways.

(a) A of pond = 5*3 = 15 m^2
Click to expand...
Yes.

njbeep said:
(b)Now i start to get a little unstuck, i think (b) should look something like this:

(3+2y)(5+2y) + 15
Click to expand...
Why? By what logic did you obtain this expression? For instance, you started by drawing the rectangle for the pond, labelling the sides with their given dimensions. Then you drew another, larger rectangle around the first, labelling the width. Then you labelled the outside of the larger rectangle with its dimensions, which you found by adding the smaller rectangle's dimensions to the widths, etc. You multiplied these dimension expressions and... then what?

njbeep said:
(c) I am entirely uncertain what should happen with (c) and i would appreciate greatly an explanation.
Click to expand...
If the expression from (b) is the area of the pond and the pathway, and if the value from (a) is the area of the pond only, then how would one find the area of the pathway only? (Hint: Subtract.) ;)
 
stapel said:
Yes.


Why? By what logic did you obtain this expression? For instance, you started by drawing the rectangle for the pond, labelling the sides with their given dimensions. Then you drew another, larger rectangle around the first, labelling the width. Then you labelled the outside of the larger rectangle with its dimensions, which you found by adding the smaller rectangle's dimensions to the widths, etc. You multiplied these dimension expressions and... then what?
Click to expand...

So from what you've said here, is b) more like A= (3+y)(5+y)?
 
stapel said:
How did you get this from your picture?

Please be complete. Thank you! ;)
Click to expand...

Because the area of the inside square is 5x3, and the outside square is +y meters wider. So we end up being able to 5x3=15 + yxy (or the area of y).

I can see from your last comment how we can get c (we're going to subtract (a) from (b) and get only the pathway. ;)
 
njbeep said:
Because the area of the inside square is 5x3, and the outside square is +y meters wider. So we end up being able to 5x3=15 + yxy (or the area of y).
Click to expand...
No; the above equation isn't even true. :shock:

Isn't the pathway on all four sides of the pond? So why are you adding "y" to each dimension? What does your drawing show? ;)
 
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