A rectangle has length 9.3 x
102 cm and width 8.1 x 10
cm. Which of these statements are true?
The area of the rectangle is 7.533 x 10^4 cm^2? True or false
The perimeter of the rectangle is 1.71 × 10^3 cm? True or false
The length of the rectangle is approximately 1.15 × 10
times greater than the width? true or false
The length of the rectangle squared is approximately 8.65 × 10^5? true or false
First, let's calculate the area and perimeter of the rectangle:
Area = length x width
Area = (9.3 x 10^2 cm) x (8.1 x 10 cm)
Area = 75.33 x 10^3 cm^2
Perimeter = 2(length + width)
Perimeter = 2((9.3 x 10^2 cm) + (8.1 x 10 cm))
Perimeter = 34.8 x 10^2 cm = 3.48 x 10^3 cm
Now, let's check the statements:
1. The area of the rectangle is 7.533 x 10^4 cm^2:
True. The actual area of the rectangle is 75.33 x 10^3 cm^2, which can be simplified to 7.533 x 10^4 cm^2.
2. The perimeter of the rectangle is 1.71 × 10^3 cm:
False. The actual perimeter of the rectangle is 3.48 x 10^3 cm.
3. The length of the rectangle is approximately 1.15 × 10 times greater than the width:
False. The length is 9.3 x 10^2 cm and the width is 8.1 x 10 cm. The ratio of length to width is approximately 11.48, not 1.15.
4. The length of the rectangle squared is approximately 8.65 × 10^5:
False. The length squared would be (9.3 x 10^2 cm)^2 = 8.649 x 10^5 cm^2, not 8.65 x 10^5 cm^2.
Therefore, only the first statement is true.