# Thread: Find Width of Floor Mat

1. ## Find Width of Floor Mat

Jason paints with watercolors on a sheet of paper 29 inches wide by 13 inches high. He then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 124 inches. How wide is the strip of the mat showing around the picture?

2. Hello, fdrhs1984!

A mat around a painting has nothing to do with carpeting . . .

Jason paints with watercolors on a sheet of paper 29 inches wide by 13 inches high.
He then places this sheet on a mat so that a uniformly wide strip of the mat
shows all around the picture.
The perimeter of the mat is 124 inches.
How wide is the strip of the mat showing around the picture?

I don't suppose you made a sketch . . .

Code:
      : x :   29   : x :
- *---*--------*---*   -
x |   :        :   |   :
- | - *--------* - |   :
|   |        |   |   :
|   |        |   |   :
13 |   |13      |   | 2x+13
|   |        |   |   :
|   |   29   |   |   :
- | - *--------* - |   :
x |   :        :   |   :
- *---*--------*---*   -
: - -  2x+29 - - :

Can you see what's going on?

The painting is 29 by 13 inches.
There is an $\,x$-inch strip of mat around the painting.

Then the width of the mat is $2x+29$ inches.
And the height of the mat is $2x + 13$ inches.

The perimeter of the mat is 124 inches.

Can you write an equation now?

3. Hello Soroban!

Thanks for your help. The equation is (2x + 29)(2x + 13) = 124.

I can do it now. Thanks a lot!