Find the Hypotenuse AC in Right Triangle with Legs AB = 5 and BC = 5

To solve the problem, we'll follow these steps:

• Step 1: Identify the given sides as the legs of the right triangle.
• Step 2: Use the Pythagorean theorem, $a^2 + b^2 = c^2$, where the legs $a$ and $b$ are both 5 units.
• Step 3: Calculate $c$ using the formula and determine AC.

Let's work through the solution in detail:
Step 1: We have a right triangle with sides $AB = 5$ and $BC = 5$. These represent the legs of the triangle.

Step 2: According to the Pythagorean theorem, the hypotenuse $AC = c$ can be calculated as follows:

$a^2 + b^2 = c^2$
Substituting the values $a = 5$ and $b = 5$:
$5^2 + 5^2 = c^2$

Step 3: Calculate:

$25 + 25 = c^2$
$50 = c^2$
To find $c$, take the square root of both sides:
$c = \sqrt{50}$

Therefore, the length of AC is $\sqrt{50}$.