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

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

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## Thursday, October 20, 2016

### Geometry Problem 1275 Equilateral Triangle, Perpendicular, Projection, Metric Relations, Measurement

Labels:
equilateral,
measurement,
metric relations,
perpendicular,
projection,
triangle

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If the side of the equilateral triangle be a, then AF = (a+2)/2 and GC = (a-5)/2

ReplyDeleteSo x = a - (a+2)/2 - (a-5)/2 = 3/2

Sumith Peiris

Moratuwa

Sri Lanka

Problem 1275

ReplyDeleteSuppose that the DF intersects the BC at H, and BK is altitude of triangle ABC (K located on the side AC) ,and HL perpendicular of BK .Then <BDH=60=<BHD so BH=BD=2 and HE=

BE-BH=5-2=3.Is <LBH=30 so LH=BH/2=2/2=1=KF.So BH/KF=HE/FG or 2/1=3/x or x=3/2.

APOSTOLIS MANOLOUDIS 4 HIGH SCHOOL KORYDALLOS PIRAEUS GREECE

Let BC and DF intersect at H.

ReplyDeleteThen BH=BD=2, HE=3.

Hence, FG=x=3/2.