perplexus.info :: Geometry : A unique Heronian triangle

A unique Heronian triangle (Posted on 2017-08-05)

Find analytically, the Heronian triangle with area 24.

No Solution Yet Submitted by Jer

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re(2): easy - spoiler

| Comment 3 of 6 |

(In reply to re: easy - spoiler by broll)

Hi broll,

It's neither D4 nor D3:

the area implies a*b=48

wlog assume a<b

so only 5 values are to be tested (i.e. 1,2,3,4,6)

to cause a^2+(48/a)^2 to be a square number

ONLY 6 FITS, THEREFORE (6,8,10) =THE SIDES OF OUR TRIANGLE

Edited on August 6, 2017, 6:01 am

Posted by Ady TZIDON on 2017-08-06 06:00:14

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