Question

find the length of the third side. if necessary, write in simplest radical form.
2√41
10
answer attempt 1 out of 2
submit answer

Explanation:

Step1: Apply Pythagorean theorem

Let the third side be \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (where \(c\) is the hypotenuse). Here \(c = 2\sqrt{41}\), \(a = 10\), and \(b=x\). So \((2\sqrt{41})^{2}=10^{2}+x^{2}\).

Step2: Simplify the equation

First, \((2\sqrt{41})^{2}=4\times41 = 164\) and \(10^{2}=100\). The equation becomes \(164=100 + x^{2}\).

Step3: Solve for \(x^{2}\)

Subtract 100 from both sides: \(x^{2}=164 - 100=64\).

Step4: Find \(x\)

Take the square root of both sides: \(x=\sqrt{64}=8\).

Answer:

\(8\)