How many Distinct triangles can be formed of perimeter 44 when each side is a multiple of 4?

each side is of the for 4k, So any side we just need to find all possible values of K We can also do this by dividing the perimeter by 4 and the sides will be the values of k So now we have perimeter as 11. use the formula for the number of triangles that can be formed by given perimeter and get the result Then answer i am getting with the above appraoch is 2 Let me know if it is right answer

No, The answer is not right. The correct answer is 12

The answer should be 4. You can try all possibilities, will end up only getting (4,20,20),(8,16,20),(12,12,20) and (12, 16, 16)

Let 4a, 4b, 4c be the sides of triangle. Then, 4(a+b+c)=44 => a+b+c=11. We know that a+b>c & a+b+c=11 => c<5.5 (1)c=5 => a+b=6. Thus pairs satisfying this are (1,5), (2,4), (3,3). (2)c=4 => a+b=4. Pairs are (2,5), (3,4). (3)c=3 => a+b=8. Pairs are (4,4), (3,5). (4)c=2 => a+b=9. Pair possible is (4,5). (5)c=1 => a+b=10. Pair possible is (5,5). Thus, according to my logic, the answer is 9. I may be wrong as well.