Question

r answers in exact form. 6) what patterns do you notice?

Explanation:

Step1: Identify the triangle type

This is a right - isosceles triangle since the two legs are equal (marked with the same tick marks), so \(x = y\).

Step2: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\). Here \(a = x\), \(b = y\) (and \(x = y\)), and \(c=10\sqrt{2}\). So \(x^{2}+y^{2}=(10\sqrt{2})^{2}\). Substituting \(y = x\), we get \(x^{2}+x^{2}=200\), which simplifies to \(2x^{2}=200\).

Step3: Solve for \(x\)

Divide both sides of \(2x^{2}=200\) by 2: \(x^{2}=100\). Taking the square root of both sides and considering the length is non - negative, \(x = 10\). Since \(y = x\), \(y = 10\).

Answer:

\(x = 10\)
\(y = 10\)