Answer:
120 square inches.
Explanation:
Let's call the length of the picture frame "L" and the width "W". We know that the perimeter is the sum of all sides, so we can write an equation in terms of L and W:
Perimeter = 2L + 2W = 46
We also know that the width is 7 inches shorter than the length, so we can write another equation:
W = L - 7
Now we can substitute the second equation into the first equation to get:
2L + 2(L - 7) = 46
Simplifying this expression, we get:
4L - 14 = 46
Adding 14 to both sides, we get:
4L = 60
Dividing by 4, we get:
L = 15
Now we can use the second equation to find W:
W = L - 7 = 15 - 7 = 8
So the length is 15 inches and the width is 8 inches. To find the area of the picture frame, we multiply the length by the width:
Area = L * W = 15 * 8 = 120 square inches
Therefore, the area of the picture frame is 120 square inches.