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

Here, assume the legs have length $a$ and the hypotenuse is 8. Also, if one of the legs is $x$, and using the ratio, if the hypotenuse $c = 8$ and $c=a\sqrt{2}$, then $a=\frac{c}{\sqrt{2}}$. Rationalize the denominator: $a=\frac{8}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{8\sqrt{2}}{2} = 4\sqrt{2}$.

Answer:

$x = 4\sqrt{2}$