select the correct answer. what is the value of x in the triangle? 3√2 x a. 3√2 b. 3 c. 6 d. 6√2 e. 2√2

Explanation:

Step1: Identify the triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the ratio of the sides is $1:1:\sqrt{2}$, where the legs are of equal length and the hypotenuse is $\sqrt{2}$ times the length of a leg.

Step2: Set up the relationship

Let the length of each leg be $a$ and the hypotenuse be $c$. The formula is $c = a\sqrt{2}$. Here, $c = 3\sqrt{2}$ and we want to find $a$ (which is $x$). We have $3\sqrt{2}=x\sqrt{2}$.

Step3: Solve for $x$

Divide both sides of the equation $3\sqrt{2}=x\sqrt{2}$ by $\sqrt{2}$. So, $x = 3$.

Answer:

B. 3