Arectangular stained glass window is 2 feet by 4 feet. a clear glass border is constructed around the stained glass window. the width of the border is equal and was made out of 7 square feet of clear glass. what is the width of the border?

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.

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step-by-step explanation:

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step-by-step explanation: