Question

find the length of side ( x ) to the nearest tenth.
answer attempt 1 out of 2
( x = )

Explanation:

Step1: Identify triangle type

This is an isosceles right triangle, so the two legs (including $x$) are equal, and the hypotenuse is $\sqrt{6}$.

Step2: Apply Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$. Here $a = b = x$, $c = \sqrt{6}$.
$$x^2 + x^2 = (\sqrt{6})^2$$

Step3: Simplify the equation

Combine like terms and calculate the right-hand side:
$$2x^2 = 6$$

Step4: Solve for $x^2$

Divide both sides by 2:
$$x^2 = \frac{6}{2} = 3$$

Step5: Solve for $x$

Take the square root of both sides (length is positive):
$$x = \sqrt{3} \approx 1.7$$

Answer:

$x \approx 1.7$