To determine if the sticks can form a right triangle, we can use the Pythagorean theorem. For three lengths \(a\), \(b\), and \(c\) (where \(c\) is the longest side), a right triangle can be formed if the following condition holds:
\[ a^2 + b^2 = c^2 \]
Given the stick lengths are 10 cm, 11 cm, and 13 cm, we identify the longest stick (13 cm) as \(c\), and the other two sticks (10 cm and 11 cm) as \(a\) and \(b\).
Now, we calculate:
- \(a^2 = 10^2 = 100\)
- \(b^2 = 11^2 = 121\)
- \(c^2 = 13^2 = 169\)
Now, we check if \(a^2 + b^2 = c^2\):
\[ 100 + 121 = 221 \] \[ c^2 = 169 \]
Since \(221 \neq 169\), the condition does not hold. Therefore, they cannot form a right triangle.
The correct response is: No, because 100+121 does not equal 169.