Question

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Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, if the two legs are \(a = 10\) and \(b = 24\), and the hypotenuse is \(x\), the Pythagorean theorem is \(a^{2}+b^{2}=x^{2}\).
So \(x^{2}=10^{2}+24^{2}\)

Step2: Calculate the squares

\(10^{2}=100\) and \(24^{2}=576\), then \(x^{2}=100 + 576=676\)

Step3: Find the value of \(x\)

Take the square - root of both sides. Since \(x>0\) (as it represents the length of a side of a triangle), \(x=\sqrt{676}=26\)

Answer:

26