To determine the truthfulness of the statements about the rectangle, we need to calculate the area, the perimeter, and compare the dimensions.
- 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:
- True
- False
- True
- True
1 answer