Question

a triangle has sides of length 8, 10, and x. what value of x makes it the hypotenuse of a right triangle? type your answer in the box.

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, if \(x\) is the hypotenuse, then \(a^{2}+b^{2}=x^{2}\) (where \(a = 8\) and \(b = 10\)).
So, \(x^{2}=8^{2}+10^{2}\).

Step2: Calculate \(8^{2}+10^{2}\)

\(8^{2}=64\) and \(10^{2}=100\). Then \(8^{2}+10^{2}=64 + 100=164\).

Step3: Solve for \(x\)

Since \(x^{2}=164\), then \(x=\sqrt{164}\). Simplify \(\sqrt{164}=\sqrt{4\times41}=2\sqrt{41}\approx 12.8\).

Answer:

\(2\sqrt{41}\) (or approximately \(12.8\))