Question

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

Explanation:

Step1: Identify 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 hypotenuse $c$ and the legs $a$ and $b$ are related by $c = a\sqrt{2}=b\sqrt{2}$.

Step2: Set up the equation

Let the length of the leg be $x$ and the hypotenuse be $3\sqrt{2}$. Using the 45 - 45 - 90 triangle ratio formula $c = a\sqrt{2}$, we substitute $c = 3\sqrt{2}$ and $a=x$. So, $3\sqrt{2}=x\sqrt{2}$.

Step3: Solve for $x$

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

Answer:

B. 3