In a 5x5 grid, 38 isosceles triangles can be formed by connecting dots with base lengths of 1, 2, and 3. The count is obtained by considering each possible base length.
In a 5x5 grid of dots, isosceles triangles can be formed by connecting three dots in a way that two sides have equal length. To count them, categorize based on their base length.
Base of Length 1:
For each dot in the grid, there are two dots directly above it in the same column. Therefore, for each of the 5 columns, we can form 2 isosceles triangles. This gives us a total of 5 x 2 = 10 triangles.
Base of Length 2:
Similarly, for each pair of adjacent dots in a row, we can form an isosceles triangle. Since there are 4 rows and each row has 4 pairs of adjacent dots, we get 4 x 4 = 16 triangles.
Base of Length 3:
For each set of three consecutive dots in a row, we can form an isosceles triangle. There are 3 such sets in each row, and since there are 4 rows, we get 3 x 4 = 12 triangles.
Adding these up, we have a total of 10 + 16 + 12 = 38 isosceles triangles that can be formed in a 5x5 grid of dots.
The question probable may be:
How many isosceles triangles can be formed out of a 5 X 5 grid of dots?