Question
The area of a square garden is 200 m^2. How long is the diagonal?
a. 20 m
b. 15 m
c. 400 m
d. 100 m
a. 20 m
b. 15 m
c. 400 m
d. 100 m
Answers
GPT-4o mini
To find the diagonal of a square garden, we first need to determine the length of one side of the square. The area of a square is given by the formula:
\[
\text{Area} = \text{side}^2
\]
Given that the area is 200 m², we can find the side length:
\[
\text{side} = \sqrt{\text{Area}} = \sqrt{200} \approx 14.14 \, \text{m}
\]
Next, we can use the side length to find the diagonal of the square. The formula for the diagonal \( d \) of a square is:
\[
d = \text{side} \times \sqrt{2}
\]
Substituting the value we found for the side:
\[
d = 14.14 \times \sqrt{2} \approx 14.14 \times 1.414 \approx 20 \, \text{m}
\]
Thus, the length of the diagonal is approximately 20 m.
Therefore, the answer is:
**a. 20 m**
\[
\text{Area} = \text{side}^2
\]
Given that the area is 200 m², we can find the side length:
\[
\text{side} = \sqrt{\text{Area}} = \sqrt{200} \approx 14.14 \, \text{m}
\]
Next, we can use the side length to find the diagonal of the square. The formula for the diagonal \( d \) of a square is:
\[
d = \text{side} \times \sqrt{2}
\]
Substituting the value we found for the side:
\[
d = 14.14 \times \sqrt{2} \approx 14.14 \times 1.414 \approx 20 \, \text{m}
\]
Thus, the length of the diagonal is approximately 20 m.
Therefore, the answer is:
**a. 20 m**