perplexus.info :: Geometry : Matching Isosceles and Right Triangle

Matching Isosceles and Right Triangle (Posted on 2016-02-19)

Find a pair of triangles, one is a right triangle and one is an isosceles triangle, subject to the following conditions:
1) Both triangles have integer sides.
2) Both triangles have the same perimeter
3) Both triangles have the same integer area.

Submitted by Brian Smith

Rating: 4.0000 (1 votes)

Solution: (Hide)

The pair of triangles consists of an isosceles triangle with sides (132, 366, 366) and a right triangle with sides (135, 352, 377). They both have perimeter 864 and area 23,760.

It turns out that this is the only pair of triangles - this page has a link to a pdf file proving the solution is unique, up to trivial scaling.

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

Subject	Author	Date
Google search (spoiler)	Steve Herman	2016-02-22 07:53:44
A solution	Steve Herman	2016-02-22 07:39:16
re: An idea	Jer	2016-02-21 22:13:27
An idea	Jer	2016-02-20 16:18:39
hint- possible start	Ady TZIDON	2016-02-20 01:39:51
re: Matching isosceles triangles	Ady TZIDON	2016-02-20 00:12:37
Matching isosceles triangles	Steve Herman	2016-02-19 22:49:57

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