The Width of a Walkway Surrounding a GardenDate: 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/ |
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