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Answer :
Final answer:
The width of the carpet is 43 inches and the length is 65 inches.
Explanation:
Let's first assign variables to the dimensions of the carpet. Let x represent the width of the carpet. According to the given information, the length is 22 inches more than the width, so the length can be represented as x + 22.
Now let's use the formula for the perimeter of a rectangle, which is P = 2(l + w). Since we are given the perimeter of the carpet, which is 216 inches, we can plug in the values we just assigned: 216 = 2(x + x + 22).
Simplifying the equation, we have 216 = 2(2x + 22). Distributing the 2 on the right side, we get 216 = 4x + 44. Subtracting 44 from both sides, we have 172 = 4x. Dividing both sides by 4, we find x = 43.
So the width of the carpet is 43 inches, and the length is x + 22, which is 43 + 22 = 65 inches. Therefore, the dimensions of the carpet are 43 inches by 65 inches.
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