45 45 90 Triangle - Fill Online, Printable, Fillable, Blank ... - Free Printable

Let’s look at the problem carefully.

We are told that there is a pattern of red dots arranged in two vertical columns — left and right. The top row has one dot on the left and one on the right. Then, as we go down, sometimes only the left side has a dot, sometimes only the right, and sometimes both.

But wait — actually, looking again: every row has exactly one red dot — either on the left or on the right. There are 7 rows total (counting from top to bottom).

Let’s list them:

Row 1: Left
Row 2: Right
Row 3: Left
Row 4: Right
Row 5: Left
Row 6: Right
Row 7: Left

So it alternates: Left, Right, Left, Right, Left, Right, Left.

That’s 7 rows. Let’s count how many times “Left” appears: Rows 1, 3, 5, 7 → that’s 4 times.
“Right” appears: Rows 2, 4, 6 → that’s 3 times.

The question says: “If this pattern continues for 100 rows, how many red dots will be on the LEFT side?”

Since the pattern alternates starting with Left, then for any even number of rows, half would be Left and half Right. But 100 is even.

Wait — let’s test small numbers:

- 1 row: Left → 1 Left
- 2 rows: L, R → 1 Left
- 3 rows: L, R, L → 2 Left
- 4 rows: L, R, L, R → 2 Left
- 5 rows: L, R, L, R, L → 3 Left
- 6 rows: L, R, L, R, L, R → 3 Left

Pattern: For n rows, if n is even, number of Left dots = n/2
If n is odd, number of Left dots = (n+1)/2

Check:

n=1 (odd): (1+1)/2 = 1 ✔️
n=2 (even): 2/2 = 1 ✔️
n=3 (odd): (3+1)/2 = 2 ✔️
n=4 (even): 4/2 = 2 ✔️
n=5 (odd): (5+1)/2 = 3 ✔️
n=6 (even): 6/2 = 3 ✔️

Perfect.

Now, n = 100 → even → so Left dots = 100 / 2 = 50

Wait — but in our original 7-row example, we had 4 Lefts. According to formula: (7+1)/2 = 4 ✔️

So for 100 rows: since 100 is even, it’s 100 ÷ 2 = 50.

But let me double-check by thinking about pairs.

Every 2 rows: one Left, one Right.

So in 100 rows, there are 50 such pairs → each pair has 1 Left → so 50 Lefts.

Yes, that makes sense.

Final Answer: 50