Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a = 6\), \(b = 8\), and \(c=x\).
So, \(6^{2}+8^{2}=x^{2}\).

Step2: Calculate squares

\(6^{2}=36\), \(8^{2}=64\). Then \(36 + 64=x^{2}\).

Step3: Sum and find square root

\(36+64 = 100\), so \(x^{2}=100\). Taking square root, \(x=\sqrt{100}\).

Answer:

\(x = 10\)