Question

the triangle below is isosceles. find the length of side $x$ to the nearest tenth.
(image of an isosceles right triangle with hypotenuse $sqrt{6}$ and one leg $x$)

Explanation:

Step1: Identify equal sides

This is a right isosceles triangle, so the two legs (including $x$) are equal. Let the other leg be $x$ as well.

Step2: Apply Pythagorean theorem

The hypotenuse is $\sqrt{6}$, so use $a^2 + b^2 = c^2$.
$$x^2 + x^2 = (\sqrt{6})^2$$

Step3: Simplify the equation

Combine like terms and compute 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.
$$x = \sqrt{3} \approx 1.7$$

Answer:

$1.7$