Question

for the following right triangle, find the side length x.

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here, \(a = 10\), \(b = 24\), and \(x\) is the hypotenuse. So \(x^{2}=10^{2}+24^{2}\).

Step2: Calculate the squares

\(10^{2}=100\) and \(24^{2}=576\). Then \(x^{2}=100 + 576\).

Step3: Add the values

\(x^{2}=676\).

Step4: Find the square - root

\(x=\sqrt{676}=26\).

Answer:

26