Question

1. (triangle with 45°, 45°, right angle, sides x, y, base √10; equations: x² + x² = √10, 2x² = √10, x² = √10/2, √x² = √(5/2)?, x = √5/2? y = 2√5? (some crossed - out and written - over steps))

Explanation:

Step1: Apply Pythagorean theorem

$$x^2 + y^2 = (\sqrt{10})^2$$

Step2: Note equal legs (45-45-90 triangle)

Since the triangle has two 45° angles, it is an isosceles right triangle, so $x = y$. Substitute $y=x$ into the equation:
$$x^2 + x^2 = 10$$

Step3: Simplify and solve for $x$

$$2x^2 = 10$$
$$x^2 = 5$$
$$x = \sqrt{5}$$

Step4: Find $y$ (equal to $x$)

$$y = x = \sqrt{5}$$

Answer:

$x = \sqrt{5}$, $y = \sqrt{5}$