Question

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

Explanation:

Step1: Identify triangle type

This is an isosceles right triangle: the two non-right angles are equal, so the legs opposite them are congruent. The hypotenuse is $3\sqrt{2}$, and $x$ is one of the legs.

Step2: Use Pythagorean theorem

Let the legs be $x$ (both legs are equal). The Pythagorean theorem states:
$$x^2 + x^2 = (3\sqrt{2})^2$$

Step3: Simplify the equation

Combine like terms and compute the right-hand side:
$$2x^2 = 9 \times 2$$
$$2x^2 = 18$$

Step4: Solve for $x^2$

Divide both sides by 2:
$$x^2 = 9$$

Step5: Solve for $x$

Take the positive square root (length is positive):
$$x = \sqrt{9} = 3$$

Answer:

B. 3