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急！數學英文題！

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http://a367.yahoofs.com/hkblog/__DOT__yw2RIGZAgIc_EmPTRigUFIT__DOT__zcE_1/blog/20100825123131765.jpg?ib_____D_h8lC3yh (請到網址觀看圖片) In the figure, ABC is a triangle with BC = AD = 18cm. If MNPQ is a square such that QM lies on BC, P lies on AB and N lies on AC, find the area of square PQMN. (回答時需列步驟)

最佳解答:

Q同M之間果點係唔係D黎..? 點解會有2個P點 -- 2010-08-25 13:38:17 補充： ( 假設Q同M中間果點係D先...) let QM = PQ = x , E be the interception point of PN and AD Area of triangle APN = AE * PN / 2 = x(18-x)/2 Area of triangle PQB+NMC : BQ*PQ/2 + MC*MN/2 = (BQ+MC)*MN/2 = x(18-x)/2 x(18-x)/2 + x(18-x)/2 + x^2 = 18 * 18 / 2 18x-x^2+18x-x^2+2x^2=324 36x=324 x=9 area of PQMN = 9*9 = 81 cm^2

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如果D 係Q同M之間 Consider △APN and △ABC, ∠PAN=∠BAC ( common angle) ∠APN=∠ABC ( corr. ∠s, PN//BC) ∠ANP=∠ACB ( corr. ∠s, PN//BC) ∴ △APN ~ △ABC (AAA) Let E be the interception point in which line AD is perpendicular to line PN AE/AD=PN/BC (corr. sides, ~△s) AE/18=PN/18 AE=PN ∵ MNPQ is a square ∴ AE=PN=ED AD=AE+ED 18=ED+ED 18=2ED ED=9 Area of MNPQ= ED X ED =9X9= 81 HOPE IT HELPFUL63D0B758E2D502CC