Question

find the length of side $x$ to the nearest tenth.
triangle image: right - angled, with hypotenuse 3, and the two legs (including $x$) marked as equal (isosceles right triangle)

Explanation:

Step1: Identify triangle properties

This is an isosceles right triangle: legs are equal ($x$ each), hypotenuse = 3. Use Pythagorean theorem: $a^2 + b^2 = c^2$.

Step2: Substitute values into theorem

$$x^2 + x^2 = 3^2$$

Step3: Simplify the equation

$$2x^2 = 9$$
$$x^2 = \frac{9}{2}$$

Step4: Solve for x and round

$$x = \sqrt{\frac{9}{2}} = \frac{3}{\sqrt{2}} \approx 2.1$$

Answer:

2.1