Find he number of distinct triangles with integer sides and perimeter 10 that can be constructed.
1,1,8
1,2,7
...
1,4,5
all bad, because each side must be less than the sum of the other two sides.
So, list all the other possibilities and check them out.
Then would it be 2 distinct triangles?
That's what I get.
2,4,4
3,3,4
Same. Thank you
To find the number of distinct triangles with integer sides and a perimeter of 10, we can use the concept of counting.
First, let's denote the three sides of a triangle as a, b, and c, where a ≤ b ≤ c. Since the perimeter is 10, we have:
a + b + c = 10.
Now, let's list all the possibilities for a, b, and c:
If a = 1, the possible values for b and c are (1, 1, 8) and (1, 2, 7).
If a = 2, the possible values for b and c are (2, 2, 6) and (2, 3, 5).
If a = 3, the only possible values for b and c are (3, 3, 4).
So, we have a total of 5 distinct triangles:
(1, 1, 8)
(1, 2, 7)
(2, 2, 6)
(2, 3, 5)
(3, 3, 4)
Hence, there are 5 distinct triangles with integer sides and a perimeter of 10.