Let's evaluate each statement one by one.
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The area of the rectangle is 7.533×10^4 cm².
The area \( A \) of a rectangle is given by the formula: \[ A = \text{length} \times \text{width} \] Substituting the given values: \[ A = (9.3 \times 10^2) \times (8.1 \times 10) \] \[ = 9.3 \times 8.1 \times 10^{2+1} \] \[ = 75.33 \times 10^3 \] \[ = 7.533 \times 10^4 \text{ cm}^2 \] True.
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The perimeter of the rectangle is 1.71×10^3 cm.
The perimeter \( P \) of a rectangle is given by: \[ P = 2 \times (\text{length} + \text{width}) \] Substituting the given values: \[ P = 2 \times (9.3 \times 10^2 + 8.1 \times 10) \] First, convert the width to the same order of magnitude: \[ 8.1 \times 10 = 8.1 \times 10^1 = 0.081 \times 10^2 \] Now, adding: \[ 9.3 \times 10^2 + 0.081 \times 10^2 = (9.3 + 0.081) \times 10^2 = 9.381 \times 10^2 \] Now calculating the perimeter: \[ P = 2 \times 9.381 \times 10^2 = 18.762 \times 10^2 = 1.8762 \times 10^3 \text{ cm} \] False. (It should be approximately 1.88×10^3 cm)
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The length of the rectangle is approximately 1.15×10 times greater than the width.
To find this, we can calculate the ratio of the length to the width: \[ \text{Ratio} = \frac{\text{length}}{\text{width}} = \frac{9.3 \times 10^2}{8.1 \times 10} = \frac{9.3}{8.1} \times 10^{2-1} \] \[ = \frac{9.3}{8.1} \times 10 \approx 1.1481 \times 10 \] Thus, it is approximately 1.15×10 times greater. True.
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The length of the rectangle squared is approximately 8.65×10^5.
Calculate the square of the length: \[ (\text{length})^2 = (9.3 \times 10^2)^2 = 9.3^2 \times (10^2)^2 \] \[ = 86.49 \times 10^4 = 8.649 \times 10^5 \] True.
Summary of the statements:
- True
- False
- True
- True
1 answer