Question

solve for x. leave your answer in simplest radical form.
answer attempt 1 out of 2
x =

Explanation:

Step1: Create a right - angled triangle

Extend the sides to form a right - angled triangle. The vertical side of the right - angled triangle is \(10 - 6=4\), and the horizontal side is \(10\).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 4\), \(b = 10\), and \(c=x\).
So \(x=\sqrt{4^{2}+10^{2}}\).

Step3: Simplify the expression

First, calculate \(4^{2}+10^{2}=16 + 100=116\).
Then, factorize \(116=4\times29\).
So \(x=\sqrt{4\times29}=\sqrt{4}\times\sqrt{29}=2\sqrt{29}\).

Answer:

\(2\sqrt{29}\)