Word Problem: Length of a rectangle.

[silverdragon316]

This is my problem:


The length of a rectangle is three more than twice the width. The perimeter is 42ft. Find the dimensions.

What formula do I use?
Do I use Area: A=L times w

also, would length = X+3(2)

and the width=x

How should I go about setting it up.

 

[jwpaine]

Hey.

You can setup a system of equations.

Let L = length, and W = width

{L = 2W + 3
{2W + 2L = 42

Solve the system for L and W.
Show any and all steps.

Best of luck!

 

[silverdragon316]

ok. This is probably wrong but here goes.

I came up with.

2l=2w=42
2l=42-2w
l=42-2w/2
=21-w

Is this right so far?

 

[Mrspi]

ok. This is probably wrong but here goes.

I came up with.

2l=2w=42
2l=42-2w
l=42-2w/2
=21-w

Is this right so far?

Yes....

L = 21 - w

And L = 2w + 3

The two expressions for L must be equal to each other:

21 - w = 2w + 3

Now, can you take it from there?

 

[silverdragon316]

ok. Let see if this is right?

21-w=2w+3
18-w=2w
18=2w^2
9=w^2

This doesn't seem right. and if it is does it mean one side is 9 and the other 12?

and if so how is that three more than twice thw width?

 

[Mrspi]

ok. Let see if this is right?

21-w=2w+3
18-w=2w
18=2w^2
9=w^2

This doesn't seem right. and if it is does it mean one side is 9 and the other 12?

and if so how is that three more than twice thw width?

No....it isn't right.

21 - w = 2w + 3

You subtracted 3 from both sides (apparently):
21 - w - 3 = 2w + 3 - 3
18 - w = 2w

Now, you need to get rid of the term containing the variable on the left side. ADD w to both sides:

18 - w + w = 2w + w

And 2w + w is NOT 2w^2. It's 3w:
18 = 3w

Ok....that should give you the value of w, which is the width. And the length is 3 more than twice the width.

 

[silverdragon316]

ok,
from

18=3w does that
=6 and 3 more than twice equal 15?

so is the width 6 and the length 15?

15+15+6+6=42

 

[jwpaine]

{L = 2W + 3
{2W + 2L = 42

2W + 2(2W + 3)= 42
6W = 36
W = 6

Plug the value for W back into either equation and solve for L

L = 2(6) + 3
L = 12+3
L = 15


You are correct.