Question

for y. do not convert your answer to decimal form and rationa
ssary.
draw
12
y
45°
r work here
d the square root symbol (√□), type
oot\

Explanation:

Step1: Identify the triangle type

This is a right - angled isosceles triangle (since one angle is \(45^{\circ}\) and it's a right - triangle, so the other non - right angle is also \(45^{\circ}\)). In a right - angled isosceles triangle with legs of length \(a\) and hypotenuse \(y\), the relationship is \(y = a\sqrt{2}\) (derived from the Pythagorean theorem \(y^{2}=a^{2}+a^{2}=2a^{2}\)). Here \(a = 12\).

Step2: Calculate \(y\)

Substitute \(a = 12\) into the formula \(y=a\sqrt{2}\). So \(y = 12\sqrt{2}\).

Answer:

\(y = 12\sqrt{2}\)