Question

select the correct answer. what is the value of x in the triangle? a. 12√2 b. 24 c. 12 d. 6√2

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 legs are of equal length and the hypotenuse $c$ is related to the leg $a$ (or $b$) by $c = a\sqrt{2}$.

Step2: Set up the equation

Let the length of each leg be $x$. The hypotenuse $c = 12\sqrt{2}$. Using the formula $c=a\sqrt{2}$, we substitute $c = 12\sqrt{2}$ and $a=x$. So, $12\sqrt{2}=x\sqrt{2}$.

Step3: Solve for $x$

Divide both sides of the equation $12\sqrt{2}=x\sqrt{2}$ by $\sqrt{2}$. We get $x = 12$.

Answer:

C. 12