By solving a quadratic equation, we will see that the width is 1.4 inches.
For a rectangle of width W and length L, the surface area is:
A = W*L
In this case, the length will be the length of the picture plus twice the width of the frame, and same for the width, then if we define x as the width of the frame we have:
L = 8in + 2x
W = 6in + 2x
Then the area equation is:
A = (8in + 2x)*(6in + 2x)
Here we know that the area is 95.04 square inches, then we can write:
95.04 in² = (8in + 2x)*(6in + 2x)
Now we need to solve this for x.
95.04 in² = 48 in² + 4x² + (28in)*x
This is a quadratic equation:
48 in² + 4x² + (28in)*x - 95.04 in² = 0
4x² + (28in)*x - 47.04 in² = 0
The solutions are given by Bhaskara's formula:
[tex]x = \frac{-28 \pm \sqrt{(28)^2 - 4*4*(-47.04)} }{2*4} \\\\x = \frac{-28 \pm 39.2 }{8}[/tex]
So there are two solutions, we only care for the positive one, which is:
x = (-28+ 39.2)/8 = 1.4
This means that the width of the frame is 1.4 inches.
If you want to learn more about quadratic equations:
https://brainly.com/question/1214333
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