Final answer:
To find the dimensions of the rectangle, we can set up a system of equations. Solving this system, we find that the width of the rectangle is approximately 20.5 cm and the length is approximately 226.4 cm. The area of the rectangle, rounded to the nearest tenth, is 4640.2 cm².
Step-by-step explanation:
To solve this problem, we can set up a system of equations based on the given information. Let's assume that the width of the rectangle is 'w', and the length is 'l'. According to the problem, the length is 0.9 more than 11 times the width, so we can write the equation: l = 11w + 0.9. The perimeter of the rectangle is 493.8, which can be expressed as: 2l + 2w = 493.8.
Now, we can substitute the value of l from the first equation into the second equation to eliminate 'l'. This gives us: 2(11w + 0.9) + 2w = 493.8. Simplifying this equation, we get: 22w + 1.8 + 2w = 493.8. Combining like terms, we have: 24w + 1.8 = 493.8. Subtracting 1.8 from both sides, we get: 24w = 492. Subtracting 1.8 from both sides, we get: 24w = 491.2. Dividing both sides by 24, we get: w = 20.5.
Finally, we can substitute the value of w back into the first equation to find the length: l = 11(20.5) + 0.9 = 225.5 + 0.9 = 226.4.
Therefore, the dimensions of the rectangle are approximately w = 20.5 cm and l = 226.4 cm. The area of the rectangle can be calculated by multiplying the length and width: Area = w × l = 20.5 cm × 226.4 cm = 4640.2 cm². Rounded to the nearest tenth, the area of the rectangle is 4640.2 cm².