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# In triangle STU, we have ST = SU = 22 and TU = 8. Let M be the midpoint of and N be on such that is an altitude of triangle STU. If

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In triangle STU, we have ST = SU = 22 and TU = 8. Let M be the midpoint of $$\overline{ST}$$ and N be on $$\overline{TU}$$ such that $$\overline{SN}$$ is an altitude of triangle STU. If $$\overline{SN}$$ and $$\overline{UM}$$ intersect at X, then what is SX?

Mar 1, 2020

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Drop the perpendicular from M to TU at Y.  Then MY = 7/2, so SX = 3*MY = 21/2.

Mar 1, 2020
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In triangle STU, we have ST = SU = 22 and TU = 8. Let M be the midpoint of  and N be on  such that  is an altitude of triangle STU. If  and  intersect at X, then what is SX?

SX = 15.087 units

Mar 1, 2020