Question
What is the perimeter of a square given that the length of its diagonal is 30√2?
Answers
GPT-4o mini
To find the perimeter of a square given the length of its diagonal, we can use the relationship between the diagonal and the side length of the square.
For a square with side length \( s \), the diagonal \( d \) can be calculated using the formula:
\[
d = s\sqrt{2}
\]
Given that the length of the diagonal \( d \) is \( 30\sqrt{2} \), we can set up the equation:
\[
s\sqrt{2} = 30\sqrt{2}
\]
To find the side length \( s \), we can divide both sides of the equation by \( \sqrt{2} \):
\[
s = 30
\]
Now that we have the side length of the square, we can calculate the perimeter \( P \) of the square using the formula for the perimeter of a square:
\[
P = 4s
\]
Substituting the value of \( s \):
\[
P = 4 \times 30 = 120
\]
Thus, the perimeter of the square is \( \boxed{120} \).
For a square with side length \( s \), the diagonal \( d \) can be calculated using the formula:
\[
d = s\sqrt{2}
\]
Given that the length of the diagonal \( d \) is \( 30\sqrt{2} \), we can set up the equation:
\[
s\sqrt{2} = 30\sqrt{2}
\]
To find the side length \( s \), we can divide both sides of the equation by \( \sqrt{2} \):
\[
s = 30
\]
Now that we have the side length of the square, we can calculate the perimeter \( P \) of the square using the formula for the perimeter of a square:
\[
P = 4s
\]
Substituting the value of \( s \):
\[
P = 4 \times 30 = 120
\]
Thus, the perimeter of the square is \( \boxed{120} \).