Question

what is the value of x in the triangle? 10 10 x a. 10√2 b. 10 c. 20 d. 20√2 e. 10√3

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\). Here \(a = 10\), \(b = 10\), and \(c=x\).
So, \(x^{2}=10^{2}+10^{2}\).

Step2: Calculate \(x^{2}\)

\(x^{2}=100 + 100=200\).

Step3: Solve for \(x\)

\(x=\sqrt{200}=\sqrt{100\times2}=10\sqrt{2}\).

Answer:

A. \(10\sqrt{2}\)