Question

select the correct answer. what is the value of x in the triangle? triangle image a. $3sqrt{2}$ b. 3 c. 6 d. $6sqrt{2}$ e. $2sqrt{2}$

Explanation:

Step1: Identify triangle type and sides

This is a right isosceles triangle: the two non-right angles are equal, so the legs (one is $x$, the other is congruent to it) are equal, and the hypotenuse is $3\sqrt{2}$.

Step2: Apply Pythagorean theorem

For a right triangle with legs $a,b$ and hypotenuse $c$, $a^2 + b^2 = c^2$. Here $a = x$, $b = x$, $c = 3\sqrt{2}$.
$$x^2 + x^2 = (3\sqrt{2})^2$$

Step3: Simplify and solve for $x$

Combine like terms and compute the right-hand side:
$$2x^2 = 9 \times 2$$
$$2x^2 = 18$$
$$x^2 = 9$$
$$x = 3$$
(We take the positive root since length is positive.)

Answer:

B. 3