Question
Quadrilateral QRST is a rhombus. What is ST?
2z
z+7
R
Q
T
S
ST=
2z
z+7
R
Q
T
S
ST=
Answers
GPT-4o mini
In a rhombus, all sides are equal in length. Therefore, if you know the lengths of the sides involving the variables, you can set them equal to find the value of \( z \).
You mentioned that \( ST = 2z \) and \( QR = z + 7 \). Since \( ST \) and \( QR \) are opposite sides of the rhombus and must be equal, we can set up the equation:
\[
2z = z + 7
\]
Now, solve for \( z \):
1. Subtract \( z \) from both sides:
\[
2z - z = 7
\]
\[
z = 7
\]
Now that we found \( z \), we can substitute it back into the expression for \( ST \):
\[
ST = 2z = 2(7) = 14
\]
Thus, the length of \( ST \) is \( \boxed{14} \).
You mentioned that \( ST = 2z \) and \( QR = z + 7 \). Since \( ST \) and \( QR \) are opposite sides of the rhombus and must be equal, we can set up the equation:
\[
2z = z + 7
\]
Now, solve for \( z \):
1. Subtract \( z \) from both sides:
\[
2z - z = 7
\]
\[
z = 7
\]
Now that we found \( z \), we can substitute it back into the expression for \( ST \):
\[
ST = 2z = 2(7) = 14
\]
Thus, the length of \( ST \) is \( \boxed{14} \).