Math Snap

STEP 1

Assumptions1. The triangle is a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle, also known as an isosceles right triangle.
. The hypotenuse of the triangle measures $22 \sqrt{}$ units.
3. In a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle, the length of the hypotenuse is $\sqrt{}$ times the length of each leg (since the legs are of equal length).

STEP 2

We can express the length of the hypotenuse in terms of the length of one leg (let's call it $a$) using the property of a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle.
$$Hypotenuse = a \sqrt{2}$$

STEP 3

Now, we can plug in the given value for the hypotenuse to solve for $a$.
$$22 \sqrt{2} = a \sqrt{2}$$

STEP 4

To solve for $a$, we can divide both sides of the equation by $\sqrt{2}$.
$$a = \frac{22 \sqrt{2}}{\sqrt{2}}$$

implify the equation to find the length of one leg of the triangle.
$$a = \frac{22 \sqrt{2}}{\sqrt{2}} =22$$So, the length of one leg of the triangle is22 units.