Final answer:
The width of the outside of the picture frame is determined by setting up the equation w * (w + 8) = 65 cm² and solving the quadratic equation. Upon factoring, we find that the width w is 5 cm, which aligns with option B.
Step-by-step explanation:
To find the width of the outside of the picture frame, let's denote the width as w centimeters. According to the problem, the length will then be w + 8 cm. The area of a rectangle is calculated by multiplying the length by the width, so we have:
w × (w + 8) = 65 cm²
Expanding this, we get a quadratic equation:
w² + 8w - 65 = 0
To solve this quadratic equation, we can factor it:
(w + 13)(w - 5) = 0
Setting each factor equal to zero gives us two possible solutions for the width:
w + 13 = 0 or w - 5 = 0
The solution w + 13 = 0 gives a negative width, which doesn't make sense in this context, so we ignore it. The second solutionw - 5 = 0 gives:
w = 5 cm
Therefore, the width of the frame is 5 cm, and that corresponds to option B.