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.

## Saturday, November 14, 2020

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

Labels:
altitude,
Geometry,
inradius,
measurement,
perpendicular,
Problem,
right triangle

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

ReplyDeleteNow 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

AED, DFC and EDF are similar.

ReplyDeleteLet 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