Quoted:
Quoted:

The perimeter of a rectangle is 25 cm greater than the sum of the length and the width. If the length is 5 cm greater than the width, what are the dimensions of the rectangle?

I guess I've been in the sun too long. What would be the formula to solve this?

P = Perimeter

L = Length

W = Width

A rectangle has 4 sides: 2 length sides and 2 width sides. The perimeter of a rectangle is the sum of all sides, or (abbreviated) 2L + 2W.

So far, we've arrived at:

1.) P = 2L + 2W
The text says that

the perimeter of this rectangle is 25cm greater than the sum of it's length and width. Another way of phrasing this is "The perimeter is the length, plus the width, plus another 25". Or:

2.) P = L + W + 25
Now that we have a decent definition of what P is supposed to be, let's substitute it in formula #1 for calculating the perimeter of our hypothetical rectangle:

3.) L + W + 25 = 2L + 2W
Hey look, now we're down to two variables:

L and

W. Sure would be nice if we could just get this down to one variable. Let's keep reading.

"...the length is 5cm greater than the width"
Sweet, I like more info. So, what they're saying is:

4.) L = W + 5
Awesome, now l know what L is supposed to be. Let's substitute

L in formula #3, shall we?

(W + 5) + W + 25 = 2(W + 5) + 2W
And let's simplify that expression:

2W + 30 = 2(W + 5) + 2W
Sweet, now all we have to do is solve for W.

W + 15 = W + 5 + W
5 + W = 15
W = 10
Awesome. Now that we know the width is 10, we just need to find the length. You might recall in formula #4, that

L = W + 5. Well...

L = 10 + 5
L = 15
Therefore, the rectangle dimensions are 15cm long, and 10cm wide. How do I know this is right? Well, let's check our work.

"The perimeter of a rectangle is 25 cm greater than the sum of the length and the width"

What's the sum of the length and width? Well, it's 25 (L=15 and W=10, remember?).

Is this 25cm greater than the perimeter? Well....

P = 2W + 2L

P = 2(10) + 2(15)

P = 50

Is 50 25cm greater than the sum of the length and width, 25? I do believe it is.

Q. E. D. Motherfuckers!