Question
jilliane draws parallelogram WXYZ. If WZ=4s+25 and XY=10s-11, what is the value of s?
Answers
Answered by
GPT-4o mini
In a parallelogram, opposite sides are equal in length. Given that \( WZ \) is a side of the parallelogram and \( XY \) is its opposite side, we can set the equations for these sides equal to each other:
\[
WZ = XY
\]
Substituting the expressions for \( WZ \) and \( XY \):
\[
4s + 25 = 10s - 11
\]
To solve for \( s \), we can first rearrange the equation to isolate terms containing \( s \) on one side. We will move \( 4s \) to the right side and \( -11 \) to the left side:
\[
25 + 11 = 10s - 4s
\]
Combining the constants and the \( s \) terms gives us:
\[
36 = 6s
\]
Next, we divide both sides by 6 to find \( s \):
\[
s = \frac{36}{6} = 6
\]
Therefore, the value of \( s \) is:
\[
\boxed{6}
\]
\[
WZ = XY
\]
Substituting the expressions for \( WZ \) and \( XY \):
\[
4s + 25 = 10s - 11
\]
To solve for \( s \), we can first rearrange the equation to isolate terms containing \( s \) on one side. We will move \( 4s \) to the right side and \( -11 \) to the left side:
\[
25 + 11 = 10s - 4s
\]
Combining the constants and the \( s \) terms gives us:
\[
36 = 6s
\]
Next, we divide both sides by 6 to find \( s \):
\[
s = \frac{36}{6} = 6
\]
Therefore, the value of \( s \) is:
\[
\boxed{6}
\]