Perimeter Equation

[dudejma]

I'm supposed to make an equation and then find the length and width of the rectangle using the perimeter formula (if you can even call it that) it gives you. The problem is:

A rectangle's length is 1 cm less than twice its width. If the length is decreased by 3 cm and the width is decreased by 2 cm, the perimeter will be 36 cm. Find the length and width of the original rectangle.

The whole decreasing part throws me for a loop. Thanks for the help!

 

[tkhunny]

Rule #1 - Name Stuff

L = the original length
W = the original width

Original Perimeter = 2*L + 2*W

"the length is decreased by 3 cm and the width is decreased by 2 cm"

2(L-3) + 2(W-2) = 36 = New Perimeter

A little algebra

2*L - 6 + 2*W - 4 = 36

It's almost done. Do you see it?

 

[dudejma]

I understand how you made the equation but I don't understand how that gives you the original length and width. I mean, I know how you made the equation. I had it written down, but I just couldn't see how it gives the original length and width.

 

[tkhunny]

*** Philosophy Warning ***

The study of mathematics is very likely to require you to think in a way to which you may not be acustomed. If you are awesome at thinking about social sciences, this awesomeness may not help you much in the study of mathematics. It may, but it may not.

*** End of Warning ***

There is a very important reason why I wrote this so clearly: Original Perimeter = 2*L + 2*W

A little more algebra

2*L - 6 + 2*W - 4 = 2*L + 2*W - 6 - 4 = 36

Do you see it yet? You may have to put pieces together - pieces that youmay not have been told explicitly might fit together, somehow.

 

[soroban]

Hello, dudejma!

A rectangle's length is 1 cm less than twice its width.
If the length is decreased by 3 cm and the width is decreased by 2 cm, the perimeter will be 36 cm.
Find the length and width of the original rectangle.

We are expected to know that, for a rectangle: .\(\displaystyle \text{Perimeter} \:=\2\times\text{Length}) + (2\times\text{Width}) \)
. . That is: .\(\displaystyle P \:=\:2L + 2W\)


Let \(\displaystyle x\) = original width.
Then \(\displaystyle 2x-1\) = original length.

The length is decreased by 3 ... .\(\displaystyle \text{New length: }\2x-1) - 3 \:=\:2x-4\)

The width is decreased by 2 .... \(\displaystyle \text{New width: }\:x - 2\)

The new perimeter is 36: .\(\displaystyle 2(2x-4) + 2(x-2) \:=\:36\)


Got it?