Question

what is the value of x? x =

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, if one leg is 8 and the hypotenuse is 10, and the other leg is \(x\), then \(x^{2}+8^{2}=10^{2}\).

Step2: Simplify the equation

We know that \(8^{2}=64\) and \(10^{2}=100\), so the equation becomes \(x^{2}+64 = 100\). Then, subtract 64 from both sides: \(x^{2}=100 - 64\), so \(x^{2}=36\).

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x\) represents the length of a side of a triangle, we consider the positive square root. \(\sqrt{x^{2}}=\sqrt{36}\), so \(x = 6\).

Answer:

6