To find the length of the diagonal of a square when the perimeter is given, follow these steps:
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Calculate the length of one side of the square: The formula for the perimeter \( P \) of a square is given by: \[ P = 4s \] where \( s \) is the length of one side of the square. Given that the perimeter is 54 cm, we can set up the equation: \[ 54 = 4s \] To find \( s \), divide by 4: \[ s = \frac{54}{4} = 13.5 \text{ cm} \]
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Calculate the length of the diagonal: The diagonal \( d \) of a square can be calculated using the formula: \[ d = s\sqrt{2} \] Substituting \( s = 13.5 \) cm into the equation: \[ d = 13.5\sqrt{2} \] Now, we need to calculate \( \sqrt{2} \): \[ \sqrt{2} \approx 1.414 \] Therefore: \[ d \approx 13.5 \times 1.414 \approx 19.1 \text{ cm} \]
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Round the result to the nearest tenth: The result is already at 19.1 cm.
The length of the diagonal of the square, rounded to the nearest tenth, is 19.1 cm.
Thus, the answer is B. 19.1cm.