Question
Quadrilateral STUV is a square. What is UV?
4b
b+42
S
T
U
V
UV=
4b
b+42
S
T
U
V
UV=
Answers
GPT-4o mini
In a square, all sides are equal in length. Therefore, if quadrilateral STUV is a square, then the length of side UV will be the same as the lengths of the other sides.
Given the information provided, you have \( UV \) as either \( 4b \) or \( b + 42 \). If you wish to find the value of \( UV \), you'll need to set these expressions equal to each other since all sides of a square are equal:
\[
4b = b + 42
\]
Now, solve for \( b \):
1. Subtract \( b \) from both sides:
\[
4b - b = 42
\]
2. Simplify:
\[
3b = 42
\]
3. Divide both sides by 3:
\[
b = 14
\]
Now you can find the length of \( UV \) using either expression. Let's use \( UV = 4b \):
\[
UV = 4(14) = 56
\]
Alternatively, you can check using the second expression:
\[
UV = b + 42 = 14 + 42 = 56
\]
In both cases, you find that:
\[
UV = 56
\]
Thus, the length of side \( UV \) is \( 56 \).
Given the information provided, you have \( UV \) as either \( 4b \) or \( b + 42 \). If you wish to find the value of \( UV \), you'll need to set these expressions equal to each other since all sides of a square are equal:
\[
4b = b + 42
\]
Now, solve for \( b \):
1. Subtract \( b \) from both sides:
\[
4b - b = 42
\]
2. Simplify:
\[
3b = 42
\]
3. Divide both sides by 3:
\[
b = 14
\]
Now you can find the length of \( UV \) using either expression. Let's use \( UV = 4b \):
\[
UV = 4(14) = 56
\]
Alternatively, you can check using the second expression:
\[
UV = b + 42 = 14 + 42 = 56
\]
In both cases, you find that:
\[
UV = 56
\]
Thus, the length of side \( UV \) is \( 56 \).