Question

1. x y 16 x = ______ y = ______

Explanation:

Step1: Identify equal - length sides

The marks on the sides indicate that the two legs of the right - triangle are equal. So \(x = 16\).

Step2: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here \(a = x=16\), \(b = 16\), and \(c = y\). Then \(y^{2}=16^{2}+16^{2}\), \(y^{2}=256 + 256=512\), \(y=\sqrt{512}=16\sqrt{2}\).

Answer:

\(x = 16\)
\(y = 16\sqrt{2}\)