Victory for the ACT Exam 16e TG Sample

510 • M ATH

EXPLANATIONS Aa ntdh-igr du easpsp” rsot raacthe gi sy.t oB ausseedt hoen “tehlei m i n a t e - information provided in the �igure, PQ is slightly shorter than PR but almost twice as long as QR . So, the length of PQ must bB ea ssel idg ho tnl yt hl ei ss se st ht iamn a8t eb, ut ht emaoprpe rtohxai nm 4a .t e perimeter of PQR T must be between 1c h6oai cneds 2e0x.c Te ph te rf oe rf o(rHe ), aclal no fbteh ee l iamn si nwaet re d . 11. (A) Mathematics/Geometry/Triangles/ Properties of Triangles CC: HSG-SRT.C.6 CCRS: ADV.G.3 Difficulty Level = 2; Teaching Time = 5–8 minutes; Purpose = Walkthrough Since the triangle is a 45° − 45° − 90° triangle, each of the two legs is equal to 1 = = = MO 2 2 2 2 2 2 2 ^ ^ h h . Since MN and NO form a right angle, use these sides as the height and base: area = = = 1 bh 2 1 2 1 2 triangle ] g . Alternatively, “eliminate-and-guess” based on the information provided in the �igure. MN and NO are the base and height of tt hh ee ot rr ei amn ,gtl he .eBs ea sl ee nd got nh st hmeuPsyt tbhoatgho br eea n less than 20 . So, the area must be less than 2 2 2 1 = ^ h . Therefore, (C) and (D) cc ahna nbcee eol fi mg ui neastsei ndg. Nc oo rwr,etchtel yr.e i s a 5 0 / 5 0 EXPLANATIONS

STUDENT TEXT, p. 186 11. In the �igure below, what is the area of MNO T ?

A. 2 1 B. 2 2 0 C D . . 1 2 0