Saturday, November 14, 2020

Geometry Problem 1484: Right Triangle, Altitude, Incircles, Inradius, Measurement

Geometry Problem 1484. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

Geometry Problem 1484: Right Triangle, Altitude, Incircles, Inradius, Measurement.

2 comments:

  1. Tr.s AED, DFC, EDF are all similar to Tr. ABC

    Now EF = BD = ac/b, AD = c^2/b and CD = a^2/b

    Hence x/(ac/b) = 3/(c^2/b) = 4/(a^2/b) from which

    x^2 /(a^2.c^2) = (3 X 4)/(a^2.c^2)

    So x = sqrt12 = 2.sqrt3

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete
  2. AED, DFC and EDF are similar.
    Let AE=a , FC=b
    => ED=(3/4)b and DF=(4/3)a
    ED/AE=x/3
    =>x=9b/4a -----(1)
    Also DF/FC=x/4
    =>x=16a/3b-----(2)
    (1)=(2)
    => a/b=3sqrt3/8

    =>x=2Sqrt3

    ReplyDelete