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 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. Let the length of each leg be $a$, and the hypotenuse be $c$. So $c = a\sqrt{2}$.

Step2: Identify given and unknown

We know the hypotenuse $c = 7\sqrt{2}$ and we want to find the length of the leg $x$. Since $c=a\sqrt{2}$, and $c = 7\sqrt{2}$, we can set up the equation $a\sqrt{2}=7\sqrt{2}$.

Step3: Solve for $x$

Dividing both sides of the equation $a\sqrt{2}=7\sqrt{2}$ by $\sqrt{2}$, we get $a = 7$. So $x = 7$.

Answer:

$7$