Question

10 multiple choice 1 point the two triangles in the picture are similar. what is the value of x?
11 multiple choice 1 point determine the exact length of side x in the triangle.

Explanation:

Step1: Apply the Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(a = 8\), \(c=15\), and \(b=x\).
So, \(x^{2}+8^{2}=15^{2}\).

Step2: Simplify the equation

\(x^{2}+64 = 225\).
Subtract 64 from both sides: \(x^{2}=225 - 64\).
\(x^{2}=161\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{161}\).

Answer:

\(\sqrt{161}\)