To determine the measure of the hypotenuse in a right triangle where one side measures 12 cm and the other side measures 5 cm, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is given by:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
Given the side lengths, [tex]\( a = 12 \)[/tex] cm and [tex]\( b = 5 \)[/tex] cm. Now, let's apply these values to the formula step by step.
1. Square the lengths of both given sides:
[tex]\[ 12^2 = 144 \][/tex]
[tex]\[ 5^2 = 25 \][/tex]
2. Add these squares:
[tex]\[ 144 + 25 = 169 \][/tex]
3. Take the square root of the sum to find the length of the hypotenuse:
[tex]\[ \sqrt{169} = 13 \][/tex]
Thus, the measure of the hypotenuse is 13 cm.
Therefore, the correct answer is:
A) 13 cm
