Sarah wants to hang a mirror in her room. the mirror and frame must have an area of 15 square feet. the mirror is 3 feet wide and 4 feet long. which quadratic equation can be used to determine the thickness of the frame, x

x^2 + 7x - 3 = 0

Step-by-step explanation:

I think you meant "width of the frame" from outside of frame to outside of mirror.

Let x represent the width of the frame.

Area of mirror is (3 ft)(4 ft) = 12 ft^2.  Total area of mirror and frame is 15 ft^2.  The 3 ft^2 difference is the area of the frame.

But you were asked to find a quadratic equation that would give you the "width" of the frame.  

The "new" width would be 3 + x and the "new" height would be 4 + x.

Then the area of the mirror and frame together would be

A = (3 + x)(4 + x) = 15 ft^2, or

      12 + 7x + x^2 = 15 ft^2, or

x^2 + 7x - 3 = 0.  This is the desired quadratic equation.

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