Question
ABCD is a square DM=22. What is the measure of AC?
(1 point)
AC=
(1 point)
AC=
Answers
GPT-4o mini
In a square, the diagonals can be calculated using the Pythagorean theorem. Let's denote the side length of the square as \( s \). The formula for the diagonal \( d \) of a square is given by:
\[
d = s\sqrt{2}
\]
From the information provided, we know that \( DM \) is 22. It's not entirely clear what \( DM \) refers to, but if we assume that \( DM \) pertains to a side length or a segment related to the square’s dimensions, then we can further interpret it.
If we assume that \( DM \) represents the side length of the square, then:
\[
s = 22
\]
We can now calculate the length of diagonal \( AC \) (which is equal to diagonal \( BD \) since it's a square):
\[
AC = s\sqrt{2} = 22\sqrt{2}
\]
Thus, the measure of \( AC \) is:
\[
AC = 22\sqrt{2}
\]
If you want a numerical approximation:
\[
22\sqrt{2} \approx 22 \times 1.414 \approx 31.11
\]
But the exact expression for \( AC \) is:
\(\boxed{22\sqrt{2}}\)
\[
d = s\sqrt{2}
\]
From the information provided, we know that \( DM \) is 22. It's not entirely clear what \( DM \) refers to, but if we assume that \( DM \) pertains to a side length or a segment related to the square’s dimensions, then we can further interpret it.
If we assume that \( DM \) represents the side length of the square, then:
\[
s = 22
\]
We can now calculate the length of diagonal \( AC \) (which is equal to diagonal \( BD \) since it's a square):
\[
AC = s\sqrt{2} = 22\sqrt{2}
\]
Thus, the measure of \( AC \) is:
\[
AC = 22\sqrt{2}
\]
If you want a numerical approximation:
\[
22\sqrt{2} \approx 22 \times 1.414 \approx 31.11
\]
But the exact expression for \( AC \) is:
\(\boxed{22\sqrt{2}}\)