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        riddles >> easy >> Number of triangles
        
(Message started by: navdeep1771 on Aug 26^th, 2021, 7:48pm)

Title: Number of triangles
Post by navdeep1771 on Aug 26^th, 2021, 7:48pm

Find the number of all integer-sided isosceles obtuse-angled triangles with perimeter 2008.

Title: Re: Number of triangles
Post by rmsgrey on Aug 27^th, 2021, 9:05am

Do you count the degenerate traingle with sides 1004/502/502?

If so, then I make it [hide]87[/hide]

Reasoning:
[hideb]a right isosceles triangle has sides in ratio 2^1/2:1:1 and 2008/(2+2^1/2) is just over 588. Since any integer length for the matching sides will give an integer length for the remaining side, any integer from 502 to 588 will give an isosceles triangle with angle greater than a right angle.[/hideb]