To find the length of the hypotenuse, [tex]\( x \)[/tex], of a right triangle with legs of length 18 and 24, we use the Pythagorean theorem. The Pythagorean theorem states:
[tex]\[ a^2 + b^2 = c^2 \][/tex]
where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are the lengths of the legs of the triangle, and [tex]\( c \)[/tex] is the length of the hypotenuse.
In this problem, given:
- [tex]\( a = 18 \)[/tex]
- [tex]\( b = 24 \)[/tex]
We substitute these values into the Pythagorean theorem to find [tex]\( x \)[/tex]:
[tex]\[ 18^2 + 24^2 = x^2 \][/tex]
The correct equation is:
[tex]\[ 18^2 + 24^2 = x^2 \][/tex]
Therefore, the correct answer is:
[tex]\[ 18^2 + 24^2 = x^2 \][/tex]
