The Width of a Walkway Surrounding a Garden

Date: 04/04/98 at 13:23:39
From: Liz Ferry
Subject: geometry

Hi, I've got a question for you!

Question: There is a garden with dimensions 24x30. There is a walkway 
that surrounds this garden that is 1/4th the area of the garden. What 
is the width of the walkway?

Help me!

Thanks,
Liz

Date: 05/04/98 at 11:46:54
From: Doctor Sonya
Subject: Re: geometry

Hello there, Liz. I'm sorry it took us so long to get to your 
question. It got stuck in one of our administrative pages, and I'm 
only now getting it out. Anyway, I hope you managed to figure out the 
answer to your question; but just in case you never did, here are some 
hints.

I drew up a diagram of the garden for you to look at as you read my 
solution. It's at:

      

The inner square is the garden, and the outer square is the garden 
plus walkway. Now, let's look at what we need to find out and what we 
know.

We want the width of the walkway (I've called it X). We know that the 
area of a rectangle in general is:

   length times width 

so the area of the garden is 24 x 30 = 740 m. sq.

How about the area of the rectangle formed by the walkway AND the 
garden? (Look at the diagram for that one.) I'll call this total area 
T. Before you go any further, you should figure out what T is. It's 
fine if you just get an equation with X's in it and not an absolute 
number. OK, great. Now you know T.

I'll call the area of the garden G and the area of the walkway W. We 
also know that:

   G + W = T

Can you tell me why? 

There is one more equation that we know:

   W = (1/4)G

Again, I'll leave it to you to tell me why we know that this is true.

I'm going to leave it to you to finish this problem. Just plug all the 
numbers that you know into the two equations, and see what happens. 
Remember that in the end, you want to find the value for X.

-Doctor Sonya, The Math Forum
Check out our web site! http://mathforum.org/dr.math/