Question

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Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here, \(a = 9\), \(b = 40\), and \(c=x\). So, \(9^{2}+40^{2}=x^{2}\).

Step2: Calculate squares

\(9^{2}=81\) and \(40^{2}=1600\). Then \(x^{2}=81 + 1600\).

Step3: Sum the values

\(x^{2}=1681\).

Step4: Find the square - root

\(x=\sqrt{1681}\), and \(\sqrt{1681}=41\).

Answer:

41