Questions: Which of the following is the missing side length that completes the Pythagorean triple below? 5,12 A. 17 B. 14 C. 13 D. 15

Solution Steps

We are given two sides of a right triangle, \(5\) and \(12\), and we need to find the missing side that completes the Pythagorean triple. The options provided are \(17\), \(14\), \(13\), and \(15\).

The Pythagorean theorem states that for a right triangle with sides \(a\), \(b\), and hypotenuse \(c\), the relationship is given by:

\[ a^2 + b^2 = c^2 \]

Given the sides \(5\) and \(12\), we assume these are the two shorter sides, and we need to find the hypotenuse \(c\).

\[ 5^2 + 12^2 = c^2 \]

Calculate \(5^2\) and \(12^2\):

\[ 5^2 = 25 \] \[ 12^2 = 144 \]

Add these values:

\[ 25 + 144 = 169 \]

Now, solve for \(c\):

\[ c^2 = 169 \implies c = \sqrt{169} = 13 \]

Final Answer