Question

correct values into the boxes:
x = 18
y = 9

Explanation:

Step1: Determine the value of \( y \)

Since the figure is a square (all sides are equal in a square), and one side is given as \( 18 \), but looking at the markings (the short lines indicating congruent segments), the side \( y \) is half of the side of the square. So \( y=\frac{18}{2}=9 \).

Step2: Calculate the value of \( x \)

Using the Pythagorean theorem \( a^{2}+b^{2}=c^{2} \) (where \( a = 18 \), \( b = 18 \) and \( c=x \)). Substitute the values: \( x=\sqrt{18^{2}+18^{2}}=\sqrt{324 + 324}=\sqrt{648}=\sqrt{324\times2}=18\sqrt{2}\approx25.46 \). But wait, no - wait, actually, if we consider the right - triangle formed with legs \( 18 \) and \( 18 \) (the side of the square is \( 18 \), and the other side of the right - triangle is also \( 18 \) because of the square's properties).

Wait, no, no! Wait, the side of the square is \( 18 \), and \( y = 9 \) (half of the side of the square). But for \( x \), using the Pythagorean theorem in the right - triangle with legs \( 18 \) and \( 18 \) (the full side of the square). \( x=\sqrt{18^{2}+18^{2}}=\sqrt{2\times18^{2}} = 18\sqrt{2}\). But if we assume that there was a mis - interpretation and it's a 45 - 45 - 90 triangle (isosceles right - triangle) with leg \( a = 18 \), then the hypotenuse \( x=a\sqrt{2}=18\sqrt{2}\). But if we consider the problem's initial wrong input (maybe a mis - drawn figure), but if we follow the Pythagorean theorem for a right - triangle with legs \( 18 \) and \( 18 \):

$$x=\sqrt{18^{2}+18^{2}}=\sqrt{324+324}=\sqrt{648}=18\sqrt{2}$$

Answer:

\( y = 9\), \(x = 18\sqrt{2}\)