Page 155 - Engineering

‫ﺍﳍﻨﺪﺳﺔ )ﺍﳉﺰء ﺍﻷﻭﻝ(‬ ‫‪١٤٢‬‬

‫)‪ (٢١‬ﰲ اﻟﺸﻜﻞ اﳌﺮﻓﻖ‪ D ،C ،B ،A ،‬ﻋﻠﻰ اﺳﺘﻘﺎﻣﺔ واﺣﺪة‪،AX BY ،‬‬
‫‪ .X = Y ،AB = CD‬ﻣﺎ ﻧﺴﺒﺔ ﻣﺴﺎﺣﺔ اﻟﺸﻜﻞ ‪ AXEB‬إﱃ ﻣﺴﺎﺣﺔ‬

‫اﻟﺸﻜﻞ ‪ DYEC‬؟‬

‫‪XY‬‬

‫‪E‬‬

‫‪A BC D‬‬

‫)أ( ‪ 1‬إﱃ ‪) 1‬ب( ‪ 2‬إﱃ ‪) 3‬ج( ‪ 1‬إﱃ ‪) 2‬د( ‪ 3‬إﱃ ‪2‬‬

‫)‪ [Mandelbrot#2] (٢٢‬اﳌﺜﻠﺚ ‪ △ABC‬ﻗﺎﺋﻢ اﻟﺰاوﻳﺔ‪ AD ،C = 90° ،‬و‬

‫‪ BE‬ﻣﺘﻮﺳﻄﺎن‪ .AB = 4 ،‬ﻣﺎ ﻗﻴﻤﺔ ‪ (AD)2 + (BE)2‬؟‬

‫)د( ‪35‬‬ ‫)ج( ‪30‬‬ ‫)ب( ‪25‬‬ ‫)أ( ‪20‬‬

‫)‪ [M and IQ 1992] (٢٣‬اﳌﺜﻠﺚ ‪ △ACB‬ﻣﺘﺴﺎوي اﻷﺿﻼع‪ CM ،‬ﻣﺘﻮﺳﻂ‪.‬‬

‫ﻋﻴﻨﺎ ﻧﻘﻄﺔ ‪ N‬ﻋﻠﻰ ‪ BC‬ﲝﻴﺚ ﻳﻜﻮن ‪ MN‬ﻋﻤﻮدﻳﺎً ﻋﻠﻰ ‪ .BC‬ﻣﺎ ﻫﻲ‬
‫اﻟﻨﺴﺒﺔ ‪ BN : BC‬؟‬

‫)د( ‪2 : 3‬‬ ‫)ج( ‪1 : 4‬‬ ‫)ب( ‪1 : 3‬‬ ‫)أ( ‪1 : 2‬‬

‫‪ .AC‬ﻣﺎ ﻗﻴﻤﺘﺎ ‪ x‬و ‪ y‬؟‬ ‫)‪ (٢٤‬ﰲ اﳌﺜﻠﺚ ‪ △ABC‬اﳌﺒﲔ أدﻧﺎﻩ‪DE ،‬‬
‫)ب( ‪y = 27 ،x = 18‬‬ ‫)أ( ‪y = 26.25 ، x = 17.14‬‬
‫)د( ‪y = 28 ،x = 19‬‬ ‫)ج( ‪y = 27.25 ، x = 18.14‬‬