To find the missing side of a right triangle using the Pythagorean theorem, you would typically use the equation \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse (the longest side), and \( a \) and \( b \) are the other two sides.
Given the responses and the numbers (where it seems like 4 and 10 might represent the two legs of a right triangle), the correct formulation for finding the missing side should be:
- \( a^2 + b^2 = c^2 \)
In this context, if we designate \( a = 4 \) and \( b = 10 \), then the equation would specifically be:
- \( 4^2 + 10^2 = c^2 \)
So, looking at your options, the following equation would be correct:
\( 4^2 + 10^2 = c^2 \)
Which matches the first response provided in your quiz format, thus:
42 + 102 = c^2 (as written, but should be clarified with proper notation as \( 4^2 + 10^2 = c^2 \)).
If \( 42 \), \( 102 \), and \( c^2 \) were meant as \( 4^2 \), \( 10^2 \), and \( c^2 \), then the first response is the one you need.