Geometry Problem. Post your solution in the comment box below.

Level: Mathematics Education, High School, Honors Geometry, College.

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## Wednesday, March 6, 2019

### Geometry Problem 1422: Triangle, Transversal, Cevian, Area, Quadrilateral, Measurement

Labels:
area,
cevian,
geometry problem,
measurement,
quadrilateral,
transversal,
triangle

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Draw altitudes: h1 from G to BD, h2 from AD, h3 from G to BE, h4 from F to EC

ReplyDeleteFrom Given S : e/c = h2/(3h1), and d/a = (8.h4)/(x.h3)

substitute h4/h3 with h2/h1 and e/c with d/a (from the given data)

=> S = 10

Let h1 = altitude from G in Tr. BDG

ReplyDeleteh2 = altitude from F in Tr. ABF

Similarly for h3 & h4 for Tr.s BEG & BCF

Let x be the required area

h1e = 14 & h2c = 42,

h3d = 16 & h4a = 2x + 16

h1/h2 = BG/BF = h3/h4

So (14/e)/(42/c) = (16/d)/((2x + 16)/a)) which gives

c/3e = 8a/(d(x+8))

Hence x + 8 = 24.ae/cd = 18

Therefore x = 10

Sumith Peiris

Moratuwa

Sri Lanka