perplexus.info :: Shapes : Square Heronian

Square Heronian (Posted on 2024-01-02)

Heronian triangle has integer sides and integer area. Find a Heronian triangle where all 3 sides are squares. Only one solution is known.

Extra credit for anyone who finds a second solution.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

As of February 2021, only two primitive Heronian triangles with perfect square sides are known:
(1853², 4380², 4427², Area=32918611718880), published in 2013.
(11789², 68104² , 68595², Area=284239560530875680), published in 2018
For an explanation, refer to the solution submitted by Charlie in this location.

Comments: ( You must be logged in to post comments.)

	Subject	Author	Date
	computer attempt; researched answer (spoiler)	Charlie	2024-01-02 13:26:33

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