Question

the triangle below is isosceles. find the length of side x to the nearest tenth.
(an isosceles right - triangle with hypotenuse (sqrt{5}) and one leg x)

Explanation:

Step1: Identify triangle properties

This is a right isosceles triangle, so the two legs are equal ($x = \text{other leg}$), and the hypotenuse is $\sqrt{5}$. Use the Pythagorean theorem: $a^2 + b^2 = c^2$.

Step2: Substitute values into theorem

Since $a = b = x$ and $c = \sqrt{5}$, substitute to get:
$$x^2 + x^2 = (\sqrt{5})^2$$

Step3: Simplify and solve for $x^2$

Combine like terms and simplify the right side:
$$2x^2 = 5$$
$$x^2 = \frac{5}{2} = 2.5$$

Step4: Solve for $x$ and round

Take the square root and round to the nearest tenth:
$$x = \sqrt{2.5} \approx 1.6$$

Answer:

1.6