Given AQRS ATUV, QS = 3v + 2 and TV = 7v – 6, find the length of QS and TV. 命 > Math symbols • Relations • Geometry » Groups ) Trigonometry » Statistics > Greek of 3 Answered O Type here to search
Given AQRS ATUV, QS = 3v + 2 and TV = 7v – 6, find the length of QS and TV. 命 > Math symbols • Relations • Geometry » Groups ) Trigonometry » Statistics > Greek of 3 Answered O Type here to search
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![**Problem Statement:**
Given that triangles \(\triangle QRS\) and \(\triangle TUV\) are congruent, with \(QS = 3v + 2\) and \(TV = 7v - 6\), find the length of \(QS\) and \(TV\).
**Instructions:**
1. Since the triangles are congruent, their corresponding sides are equal. Thus, we have:
\[
QS = TV
\]
2. Substitute the given expressions:
\[
3v + 2 = 7v - 6
\]
3. Solve the equation for \(v\):
\[
3v + 2 = 7v - 6
\]
Rearrange the equation:
\[
3v - 7v = -6 - 2
\]
\[
-4v = -8
\]
Divide both sides by \(-4\):
\[
v = 2
\]
4. Substitute \(v = 2\) back into one of the expressions to find the length of \(QS\) and \(TV\):
- For \(QS\):
\[
QS = 3(2) + 2 = 6 + 2 = 8
\]
- For \(TV\):
\[
TV = 7(2) - 6 = 14 - 6 = 8
\]
5. Therefore, the length of \(QS\) and \(TV\) is 8 units.
**Conclusion:**
Both sides \(QS\) and \(TV\) are confirmed to be equal, at a length of 8 units, which is consistent with the property of congruent triangles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F989e5910-3b6c-4653-adbe-6c4ff5177518%2Ffc1c70e9-a6c8-45fb-80a1-c69e8b9dd47c%2F8y3f79q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given that triangles \(\triangle QRS\) and \(\triangle TUV\) are congruent, with \(QS = 3v + 2\) and \(TV = 7v - 6\), find the length of \(QS\) and \(TV\).
**Instructions:**
1. Since the triangles are congruent, their corresponding sides are equal. Thus, we have:
\[
QS = TV
\]
2. Substitute the given expressions:
\[
3v + 2 = 7v - 6
\]
3. Solve the equation for \(v\):
\[
3v + 2 = 7v - 6
\]
Rearrange the equation:
\[
3v - 7v = -6 - 2
\]
\[
-4v = -8
\]
Divide both sides by \(-4\):
\[
v = 2
\]
4. Substitute \(v = 2\) back into one of the expressions to find the length of \(QS\) and \(TV\):
- For \(QS\):
\[
QS = 3(2) + 2 = 6 + 2 = 8
\]
- For \(TV\):
\[
TV = 7(2) - 6 = 14 - 6 = 8
\]
5. Therefore, the length of \(QS\) and \(TV\) is 8 units.
**Conclusion:**
Both sides \(QS\) and \(TV\) are confirmed to be equal, at a length of 8 units, which is consistent with the property of congruent triangles.
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