To solve for the length of the hypotenuse of a right triangle with leg lengths of 5 inches and 12 inches, we can use the Pythagorean theorem. This theorem states that for 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:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
In this problem, one leg (a) is given as 12 inches and the other leg (b) is 5 inches. We'll substitute these values into the Pythagorean theorem and solve for c, the hypotenuse.
1. First, square both leg lengths:
[tex]\[ 12^2 = 144 \][/tex]
[tex]\[ 5^2 = 25 \][/tex]
2. Add these squared values together:
[tex]\[ 144 + 25 = 169 \][/tex]
3. Take the square root of the result to find the length of the hypotenuse:
[tex]\[ c = \sqrt{169} \][/tex]
[tex]\[ c = 13 \][/tex]
Thus, the length of the hypotenuse of the right triangle with leg lengths of 5 inches and 12 inches is 13 inches.
So, the correct answer is:
13 inches.
