In the diagram below, start overline, U, V, end overline
UV
is parallel to start overline, R, S, end overline
RS
. If R, U, equals, 18RU=18, U, V, equals, 8UV=8, and R, S, equals, 14RS=14, find the length of start overline, U, T, end overline
UT
. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
Substituting the values given,
Cross-multiplying,
Expanding and simplifying
Combining like terms,
Subtracting ___ from both sides
Simplifying further,
Factoring
Setting each factor equal to zero
Solve: