Final answer:
The length of the painting is 24 inches and the width is 18 inches.
Step-by-step explanation:
To find the dimensions of the rectangular painting, let's set up an equation based on the given information.
Let's say the length of the painting is x inches.
According to the problem, the width of the painting is 6 less than its length, so the width would be x - 6 inches.
The perimeter of a rectangle is calculated by adding up all four sides, so we can set up the following equation:
2(x + x - 6) = 84
Simplifying the equation gives us:
2(2x - 6) = 84
4x - 12 = 84
4x = 96
x = 24
Therefore, the length of the painting is 24 inches.
To find the width, we substitute the value of x into the equation for the width:
width = x - 6 = 24 - 6 = 18
So, the width of the painting is 18 inches. From the given options, this means that statement b) The width of the painting is 18 inches. is true.