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   Author  Topic: Number of triangles  (Read 491 times)
navdeep1771
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Number of triangles  
« on: Aug 26th, 2021, 7:48pm »
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Find the number of all integer-sided isosceles obtuse-angled triangles with perimeter 2008.
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rmsgrey
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Re: Number of triangles  
« Reply #1 on: Aug 27th, 2021, 9:05am »
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Do you count the degenerate traingle with sides 1004/502/502?
 
If so, then I make it 87
 
Reasoning:
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a right isosceles triangle has sides in ratio 21/2:1:1 and 2008/(2+21/2) 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.
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