To determine the measure of the hypotenuse of a right triangle where one side measures 12 cm and the other side measures 5 cm, we can use the Pythagorean theorem. The theorem states:
[tex]\[ a^2 + b^2 = c^2 \][/tex]
Here, [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are the lengths of the two legs of the right triangle, and [tex]\( c \)[/tex] is the length of the hypotenuse. Given:
[tex]\[ a = 12 \text{ cm} \][/tex]
[tex]\[ b = 5 \text{ cm} \][/tex]
Let's substitute these values into the Pythagorean theorem:
[tex]\[ (12)^2 + (5)^2 = c^2 \][/tex]
[tex]\[ 144 + 25 = c^2 \][/tex]
[tex]\[ 169 = c^2 \][/tex]
To find [tex]\( c \)[/tex], we take the square root of both sides:
[tex]\[ c = \sqrt{169} \][/tex]
[tex]\[ c = 13 \][/tex]
Therefore, the hypotenuse of the right triangle is 13 cm.
Now, let's review the provided choices:
A) 13 cm
B) 17 cm
C) [tex]\( \sqrt{119} \)[/tex] cm
D) [tex]\( \sqrt{139} \)[/tex] cm
The correct answer is:
[tex]\[ \boxed{13 \text{ cm}} \][/tex]
