tag:blogger.com,1999:blog-6933544261975483399.post3126468453974414368..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Geometry Problem 1422: Triangle, Transversal, Cevian, Area, Quadrilateral, MeasurementAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-6933544261975483399.post-77212170220669640942019-03-06T17:30:18.073-08:002019-03-06T17:30:18.073-08:00Let h1 = altitude from G in Tr. BDG
h2 = altitude ...Let h1 = altitude from G in Tr. BDG<br />h2 = altitude from F in Tr. ABF<br />Similarly for h3 & h4 for Tr.s BEG & BCF<br /><br />Let x be the required area<br /><br />h1e = 14 & h2c = 42, <br />h3d = 16 & h4a = 2x + 16<br /><br />h1/h2 = BG/BF = h3/h4<br /><br />So (14/e)/(42/c) = (16/d)/((2x + 16)/a)) which gives<br />c/3e = 8a/(d(x+8))<br />Hence x + 8 = 24.ae/cd = 18<br />Therefore x = 10<br /><br />Sumith Peiris<br />Moratuwa<br />Sri LankaSumith Peirishttps://www.blogger.com/profile/06211995240466447227noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-32925874535279364032019-03-06T15:26:12.400-08:002019-03-06T15:26:12.400-08:00Draw altitudes: h1 from G to BD, h2 from AD, h3 fr...Draw altitudes: h1 from G to BD, h2 from AD, h3 from G to BE, h4 from F to EC<br />From Given S : e/c = h2/(3h1), and d/a = (8.h4)/(x.h3)<br />substitute h4/h3 with h2/h1 and e/c with d/a (from the given data)<br />=> S = 10 c.t.e.onoreply@blogger.com