math question: you want to mat and frame a 5x 7 photograph. The perimeter of the outside of the mat is 60 inches. the mat is twice as wide at the top and the bottom as it is on the sides. Find the dimensions of the mat

photo: 5x7

mat: 5+2*2w x 7+2*w

2(5+4w + 7+2w) = 60
w = 3

so, if the mat is 3" wide on the sides, and 6" wide top and bottom, it is 17x13 if it's a landscape. Or, it might be 19x11, if it's a portrait.

To find the dimensions of the mat, we can follow these steps:

Step 1: Let's start by assigning variables to the unknown quantities.
Let's call the width of the mat on the sides "x."
Since the mat is twice as wide at the top and bottom, the width at the top and bottom can be represented as "2x."

Step 2: Determine the length and width of the mat.
Since the photograph is 5x7 and the mat surrounds it, we need to add twice the width (2x) to the length and width of the photograph to get the overall dimensions of the mat.

Length of the mat = length of the photograph + 2 * width of mat = 7 + 2x
Width of the mat = width of the photograph + 2 * width of mat = 5 + 2(2x)

Step 3: Set up the perimeter equation.
The perimeter is the total distance around the mat. It is given as 60 inches in the question. We can use this information to set up an equation.

Perimeter = 2 * (length + width)

Substituting the calculated lengths and widths into the equation, we get:
60 = 2 * (7 + 2x) + 2 * (5 + 2(2x))

Step 4: Solve the equation to find x.
Now we can solve the equation.

60 = 2(7 + 2x) + 2(5 + 2(2x))
60 = 14 + 4x + 10 + 8x
60 = 24 + 12x
12x = 60 - 24
12x = 36
x = 36 / 12
x = 3

Step 5: Find the dimensions of the mat.
We have found the value of x, which is the width of the mat on the sides. Now, we can substitute x back into the expressions we defined earlier to find the dimensions of the mat.

Length of the mat = 7 + 2x = 7 + 2(3) = 7 + 6 = 13 inches
Width of the mat = 5 + 2(2x) = 5 + 2(2(3)) = 5 + 2(6) = 5 + 12 = 17 inches

Therefore, the dimensions of the mat are 13 inches by 17 inches.