March 28, 2015

Homework Help: for Knights

Posted by Reiny on Tuesday, January 1, 2013 at 11:49am.

have been looking at your post ...

interesting question...

let the altitude of 12 hit base a
let the altitude of 14 hit base b

then (1/2)(12)a = (1/2)(14)b
6a = 7b
a = 7b/6

let the third side be c and its altitude be x

from the properties of the sides of a triangle
c < a+b
c < 7b/6 + b
c < 13b/6

but by area property
cx = 7b or cx = 6a

take cx = 7b
the absolute maximum value that c could be is a number just a "smidgeon" less than 13b/6 , which is positive , so divide both sides of
cx = 7b by that

cx/c < 7b / (13b/6)

c < 42/13

since you want the largest integer, that would be 3

( I am a little uneasy about my last division of the inequality)

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