Final answer:
To solve for the dimensions of the rectangle, we need to set up a system of equations based on the given information. By setting up an equation for the perimeter of the rectangle and using the length equation, we can solve for the width and length of the rectangle. The width is 10.5 units and the length is 24 units.
Step-by-step explanation:
Let's denote the width of the rectangle as w. According to the problem, the length is 3 more than two times the width, so we can express it as 2w + 3. The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the width. Substituting the given values into the equation, we have 48 = 2(2w + 3 + w). Simplifying further, we get 48 = 4w + 6. Subtracting 6 from both sides, we have 4w = 42. Finally, dividing both sides by 4, we find that w = 10.5. This means that the width of the rectangle is 10.5 units. Substituting this value back into the expression for the length, we have l = 2(10.5) + 3, which simplifies to l = 24. Therefore, the length of the rectangle is 24 units.
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