Answer:
1 ft
Step-by-step explanation:
The dimensions of the stained glass window are 2 ft by 4 ft, and thus the area of this window is 8 ft².
Find the area of the composite window-with-border in a similar fashion.
Its dimensions are (2 + x) ft by (4 + x) ft, or 8 + 6x + x² ft².
Subtracting the area of the window (8 ft²) from this window-with-border area (8 + 6x + x² ft²) results in an expression for the area of the border:
8 + 6x + x² - 8 = 7 ft² of clear glass.
This simplifies to x² + 6x - 7 ft² = 0.
Solving this equation by factoring, we get:
(x + 7)(x - 6) = 0, so that either x = -7 (not possible) or x = 1.
The width of the clear glass border is 1, all around.
Check: The dimensions of the larger window-with-border are (2 + 1) by (4 + 1), or 3 by 5, or 15 ft². Those of the stained glass window are 2 by 4 ft.
15 ft² less 8 ft² is 7 ft², as given in the problem. Thus, x = 1 ft is correct.
