perplexus.info :: Numbers : Area / Perimeter Ratio

Area / Perimeter Ratio (Posted on 2024-01-04)

The triangle 5,12,13 has an area A=30 and a perimeter P=30, so A/P is 1.
The triangle 9,75,78 has an area A=324 and a perimeter P=162, so A/P is 2.

Find the smallest and largest integer-sided triangles where A/P is 10.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

Smallest Triangle: [65, 70, 75] Perimeter (P)= 210, Area(A) = 2100
Largest Triangle: [160801, 402, and 161201 ]
P = 322,404 and: A= 3,224,040
It would be observed that in both the cases: A/P =10
For an explanation, refer to:
The solution submitted by Brian Smith in this location, and:
The solution submitted by Larry in this location.

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

Subject	Author	Date
Possible maximum	Brian Smith	2024-01-05 23:25:36
re: the case for right triangles	K Sengupta	2024-01-04 15:47:55
? solution, larger found	Larry	2024-01-04 10:05:16
the case for right triangles	xdog	2024-01-04 09:20:44
partial solution	Charlie	2024-01-04 08:56:35

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