Solve "STROM" Logo Puzzle: Uniform Width Calculation

[brittney1993]

Need lots of help! :D

Homework Statement

A new rectangle with the word “STROM” is to be constructed inside the mat of an outside rectangle. The width of the mat surrounding the rectangular “STROM” logo will be the same. The area of the boundary around the word “STROM” will be the same as the logo itself. Determine the uniform width of the boundary.

Homework Equations

i made a picture of it including the measurements from the sheet:

http://img188.imageshack.us/img188/4315/strompic.jpg

The Attempt at a Solution

294.5 inches x 72 inches = 21204 inches

i really don't know what to do, please show me step-by-step directions on how to solve this so I can understand and learn from it. Thanks!:)

 

[sylas]

You'll learn even better when you show us the step by step solution! You've done the first step correctly. The units are "square inches". Now there's more information you were given. Can you find any other areas? What else has an area in this problem?

 

[brittney1993]

You'll learn even better when you show us the step by step solution! You've done the first step correctly. The units are "square inches". Now there's more information you were given. Can you find any other areas? What else has an area in this problem?

i don't know what to do :(

how am i to find the uniform width of the boundary??

 

[sylas]

i don't know what to do :(

how am i to find the uniform width of the boundary??

Step by step. Don't worry about the width yet. Can you find the area of anything else? There's the logo for example. What do you know about its area?

 

[brittney1993]

well there weren't any measurements given to the logo, so how would i go about finding its area? as far as i know, the measurements from the mat rectangle have to do with something with its area, right? i can't seem to figure it out though. =\

 

[sylas]

well there weren't any measurements given to the logo, so how would i go about finding its area? as far as i know, the measurements from the mat rectangle have to do with something with its area, right? i can't seem to figure it out though. =\

Try this sentence: "The area of the boundary around the word “STROM” will be the same as the logo itself."

Can that help tell you the area of the logo itself? You've already obtained the total area.

 

[brittney1993]

i still don't get it. :( i only got the total area which is 21204 inches. so you're saying its the same? so the logo's area is 21204 inches as well?

ah damn i suck at this...lol.

 

[sylas]

i still don't get it. :( i only got the total area which is 21204 inches. so you're saying its the same? so the logo's area is 21204 inches as well?

ah damn i suck at this...lol.

Hang in there; you're still ok. You got the first bit yourself, and now you're going to get the next.

The total area is 21204. That area is a logo, and also a fixed width boundary.The logo is the same area as the boundary, and together they equal 21204.

Whats the area of the logo? What's the area of the boundary?

Cheers -- sylas

 

[brittney1993]

10602? i divided the total area by 2.

 

[sylas]

10602? i divided the total area by 2.

That's right.

Now the next bit is going to take a bit of algebra. There are several ways of doing it but they all get the same answer.

Use a variable "w" to represent the width of the boundary. The logo is a smaller rectangle inside the big one. What is its length and width? You won't be able to give them as numbers just yet, but you can get an expressing using "w".

 

[brittney1993]

huh? I don't get it. :( so I have 10602 as the area, and now I need the legnth and width of it.

10602 = L x W

how do I get the length & width when i have the areA?

 

[sylas]

huh? I don't get it. :( so I have 10602 as the area, and now I need the legnth and width of it.

10602 = L x W

how do I get the length & width when i have the areA?

One approach I use with this sort of problem is to give variables, for everything, and then write down as many equations as I can.

For example. You have used L and W for the length and width of the logo. Now also use B for the width of the boundary.

Can you write expression using L, W and B for the length and width of the whole mat?

Length: 294.5 = ?[L,W,B]
Width: 72 = ?[L,W,B]

I'm also a big fan of drawing pictures. You can label your diagram with L, W and B, to show what lengths and widths they refer to in the problem.

 

[brittney1993]

can you just give me the answer? i know that's probably the right way to learn in ur opinion, but hear me out. if you give me the answer then i can see how you got there by going backwards. i think that'd be better because i really can't figure this out and I'm not really understanding you :(

 

[sylas]

can you just give me the answer? i know that's probably the right way to learn in ur opinion, but hear me out. if you give me the answer then i can see how you got there by going backwards. i think that'd be better because i really can't figure this out and I'm not really understanding you :(

Sorry. There are rules here about how we do this. I am probably not explaining as well as I could, and you can help me with that as well.

Here's the diagram I suggested for you, labeled with L, W and B.

Can you give n expression in terms of the variables for the total length?

294.5 = ?

 

[brittney1993]

294.5 = n

?

 

[sylas]

294.5 = n

?

That's using a new variable for the total length, and you know its value. I often use variables for known values also.

But what I am asking now is for a new expression, which captures something you know about the problem. Specifically, the total length "n" can be given in terms of your other variables L, W and B in the diagram.

n = ?

Replace the ? with an expression involving the other variables.

 

[brittney1993]

is it...

294.5 = l + 2b

72 = w + 2b

 

[sylas]

is it...

294.5 = l + 2b

72 = w + 2b

That's right!

You now have given three equations, with three unknowns. The other one is the equation you gave back in [post=2220405]msg #11[/post].

You want to find "b". You can re-arrange the two equations here into the form

L = ?
W = ?

where ? are expressions using "b". You use these expressions for L and W in your earlier equation in [post=2220405]msg #11[/post], you will have one equation, with one variable, and you have to solve that for the answer.