Question

Additional Problem: Suppose that AABC has sides AB 31,AC 35, and M is the midpoint of BC. The goal is to obtain the inequality 2 < x <33, where x AM. Construct the auxiliary lines shown, with M the midpoint of AE a. Find y-CE. Then show that 2x-AE 66. b. Show that AM (66)-33 C. Show that 2 < x < 33. (Hint: Use the Triangle Inequality in AEC. 31 35

Answer 1

0 Grven -thał Let Mbete wad pint 약 B. de A ohf Such that A-M-E dl Am ME SAS AMB EAEMC and by CPCF AB

AM +MEAE irce M2s the mid Pont of A then ME AM) AM +AMAE Prom the fguce AB 3 and AC 35 shotfidle A5 -31 and AC3) Substute A8 3 and AC AM (66) AM < 33 and ce

団. AE <66 (と) ent (AE L66 2AM L66 AE 66 AM (66):33. 2

나 . æ<33 AE +EC AC ae +31 >35