Final answer:
The width of the rectangular picture frame is 1 cm.
Step-by-step explanation:
To find the width of the rectangle, we can set up an equation using the given information. Let's say the width of the rectangle is 'w' cm. According to the problem, the length of the rectangle is 10 centimeters more than 2 times its width, which can be expressed as 2w+10 cm. The area of the rectangle is given as 20 cm^2. So, we can set up the equation: w * (2w+10) = 20 cm^2.
Simplifying the equation, we get 2w^2 + 10w - 20 = 0. Factoring the equation, we have (2w+20)(w-1) = 0. Solving for w, we find two possible values: w = -10 or w = 1. Since the width cannot be negative, the width of the rectangle is 1 cm.