isosceles triangles: perim of 25, all sides whole-number val

[tripleL2009]

How many different isosceles triangles of perimeter 25 units can be formed with all sides a whole number of units?

Any neat way to do.
Thank you!

 

[tripleL2009]

Re: isosceles triangles

so what's the theory behind the second method p-1/2 if p is odd. p-2/2 if p is even

 

[stapel]

How many different isosceles triangles of perimeter 25 units can be formed with all sides a whole number of units?

If the base (the not-equal side) has length 1, what will be the lengths of the other two sides? (Hint: Subtract 1 from 25. Then divide the result by 2.) Does this result qualify for the list? (Hint: Yes, 12 is a whole number, so 1, 12, 12, qualifies.)

If the base has length 2, what will be the lengths of the other two sides? (Hint: Use the same method as above.) Does this result qualify for the list? (Hint: No, because 23/2 = 11.5 is not a whole number.)

Continue, until you have covered the remaining possibilities.

Count up the number of cases that worked. This will be your answer. :wink:

 

[Denis]

p = perimeter

Isosceles triangles:
if p even: INT[(p-1)/4]
if p odd: INT[(p+1)/4] : INT[(25 + 1)/4] = INT[26/4] = INT[6.5] = 6

NOTES:
p > 2
includes equilaterals when p divides 3