The calculated width of the frame will be 12 cm.
How to determine the width of the frame
From the question, we have the following parameters that can be used in our computation:
Dimensions = 16 cm by 30 cm
Outside area = 312 squared cm
Let L be the length and W be the width of the rectangle.
So, we have
Area = LW
Let x be the increase in length and width.
So, we have
(16 - x)(30 - x) = 312
x² - 46x + 480 = 312
x² - 46x + 168 = 0
x² - 42x - 4x + 168 = 0
Factorize
(x - 42)(x - 4) = 0
Solve for x
x = 42 and x = 4
The value of x can be more than 16.
So, the value of x will be 4.
Then the width of the frame will be
W = 16 - x
W = 16 - 4
W = 12 cm
Hence, the width of the frame will be 12 cm.