Question

A rectangle has length 9.3×10(2)
cm and width 8.1×10
cm. Which of these statements are true?(4 points)
True False
The area of the rectangle is 7.533×104 cm2


The perimeter of the rectangle is 1.71×103 cm


The length of the rectangle is approximately 1.15×10
times greater than the width


The length of the rectangle squared is approximately 8.65×105

Answer 1

To determine the truthfulness of the statements about the rectangle, we need to calculate the area, the perimeter, and compare the dimensions.

1. **Length**: \( 9.3 \times 10^2 \, \text{cm} = 930 \, \text{cm} \)
**Width**: \( 8.1 \times 10 \, \text{cm} = 81 \, \text{cm} \)

### Area Calculation
The area \( A \) of a rectangle is given by the formula:
\[
A = \text{length} \times \text{width} = (930 \, \text{cm}) \times (81 \, \text{cm})
\]
Calculating:
\[
A = 930 \times 81 = 75330 \, \text{cm}^2 = 7.533 \times 10^4 \, \text{cm}^2
\]
**Statement 1**: The area of the rectangle is \( 7.533 \times 10^4 \, \text{cm}^2 \).
**True**

### Perimeter Calculation
The perimeter \( P \) of a rectangle is given by the formula:
\[
P = 2 \times (\text{length} + \text{width}) = 2 \times (930 \, \text{cm} + 81 \, \text{cm}) = 2 \times 1011 \, \text{cm}
\]
Calculating:
\[
P = 2 \times 1011 = 2022 \, \text{cm} = 2.022 \times 10^3 \, \text{cm}
\]
**Statement 2**: The perimeter of the rectangle is \( 1.71 \times 10^3 \, \text{cm} \).
**False**

### Length Compared to Width
We compare the length and width:
\[
\frac{930}{81} \approx 11.48
\]
Now, we check if this is approximately \( 1.15 \times 10 \):
\[
1.15 \times 10 = 11.5
\]
This indicates that the length is approximately \( 11.48 \) times greater than the width.
**Statement 3**: The length of the rectangle is approximately \( 1.15 \times 10 \) times greater than the width.
**True**

### Length Squared Calculation
Calculating \( \text{length}^2 \):
\[
\text{Length}^2 = (930)^2 = 864900
\]
We convert to scientific notation:
\[
864900 = 8.649 \times 10^5
\]
**Statement 4**: The length of the rectangle squared is approximately \( 8.65 \times 10^5 \).
**True**

### Summary:
1. True
2. False
3. True
4. True