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Given
find
the length of QS and TV.
(2 points)
△ QRS ≅△ TUV , QS = 3v + 2 and TV = 7v − 6,
To find the length of QS and TV, we first need to determine the value of v. Since triangle QRS is congruent to triangle TUV, corresponding sides are proportional.
Therefore, we can set up the proportion:
QS / TV = QR / TU
Substitute the given values:
(3v + 2) / (7v - 6) = QR / TU
Now, we need to set up another proportion using the corresponding sides QR and TU:
QR / TU = 4 / 5 (as given in the congruency of the triangles)
Therefore, we have:
(3v + 2) / (7v - 6) = 4 / 5
Cross multiply to solve for v:
5(3v + 2) = 4(7v - 6)
15v + 10 = 28v - 24
38 = 13v
v = 38 / 13
v = 2.9231 (approx.)
Now that we have found the value of v, we can substitute it back into the expressions for QS and TV:
QS = 3(2.9231) + 2
QS = 11.7693
TV = 7(2.9231) - 6
TV = 14.4617
Therefore, the length of QS is approximately 11.7693 units and the length of TV is approximately 14.4617 units.