Question

this is a 45 - 45 - 90 triangle. what is the measure of x? x = ?√

Explanation:

Step1: Recall 45 - 45 - 90 triangle ratio

In a 45 - 45 - 90 triangle, the ratio of the legs to the hypotenuse is $1:1:\sqrt{2}$. Let the length of each leg be $a$ and the hypotenuse be $c$. Then $c = a\sqrt{2}$.

Step2: Identify leg and hypotenuse

The legs of the right - angled 45 - 45 - 90 triangle are equal in length. Here, assume the length of each leg is $a$ and the hypotenuse is 8. If the length of one leg is $x$, and using the ratio $c=a\sqrt{2}$, where $c = 8$ and $a=x$. So $8=x\sqrt{2}$.

Step3: Solve for $x$

To solve for $x$, we can rewrite the equation $8=x\sqrt{2}$ as $x=\frac{8}{\sqrt{2}}$. Rationalize the denominator: $x=\frac{8\sqrt{2}}{2}=4\sqrt{2}$.

Answer:

$x = 4\sqrt{2}$