Question
The area of a rectangle is 9.312 x 10^4 cm^2 and the width is 2.56 x 10^2 cm. What is the length?
Answers
GPT-4o mini
To find the length of the rectangle, we can use the formula for the area of a rectangle, which is:
\[
\text{Area} = \text{Length} \times \text{Width}
\]
We can rearrange this formula to solve for the length:
\[
\text{Length} = \frac{\text{Area}}{\text{Width}}
\]
Given:
- Area = \(9.312 \times 10^4 \, \text{cm}^2\)
- Width = \(2.56 \times 10^2 \, \text{cm}\)
Now, substituting the values into the formula:
\[
\text{Length} = \frac{9.312 \times 10^4}{2.56 \times 10^2}
\]
To perform the division, we can divide the coefficients and then the powers of ten separately:
1. Dividing the coefficients:
\[
\frac{9.312}{2.56} = 3.64453125 \quad (\text{approximately } 3.6445)
\]
2. Dividing the powers of ten:
\[
\frac{10^4}{10^2} = 10^{4-2} = 10^2
\]
Now, multiply the two results together:
\[
\text{Length} \approx 3.6445 \times 10^2 \, \text{cm}
\]
Hence, the length of the rectangle is:
\[
\text{Length} \approx 3.6445 \times 10^2 \, \text{cm} \quad \text{or approximately } 364.45 \, \text{cm}
\]
\[
\text{Area} = \text{Length} \times \text{Width}
\]
We can rearrange this formula to solve for the length:
\[
\text{Length} = \frac{\text{Area}}{\text{Width}}
\]
Given:
- Area = \(9.312 \times 10^4 \, \text{cm}^2\)
- Width = \(2.56 \times 10^2 \, \text{cm}\)
Now, substituting the values into the formula:
\[
\text{Length} = \frac{9.312 \times 10^4}{2.56 \times 10^2}
\]
To perform the division, we can divide the coefficients and then the powers of ten separately:
1. Dividing the coefficients:
\[
\frac{9.312}{2.56} = 3.64453125 \quad (\text{approximately } 3.6445)
\]
2. Dividing the powers of ten:
\[
\frac{10^4}{10^2} = 10^{4-2} = 10^2
\]
Now, multiply the two results together:
\[
\text{Length} \approx 3.6445 \times 10^2 \, \text{cm}
\]
Hence, the length of the rectangle is:
\[
\text{Length} \approx 3.6445 \times 10^2 \, \text{cm} \quad \text{or approximately } 364.45 \, \text{cm}
\]