In a 45-45-90 triangle, the legs are of equal length, and the relationship between the lengths of the legs and the hypotenuse is defined by the Pythagorean theorem. Specifically, in a 45-45-90 triangle, the hypotenuse is equal to the length of a leg multiplied by the square root of 2.
Since both legs measure 12 cm in this case, we can calculate the length of the hypotenuse as follows:
Hypotenuse = Leg × √2
Substituting the length of the leg:
Hypotenuse = 12 cm × √2
Now, let’s compute this value:
√2 is approximately 1.414, so:
Hypotenuse ≈ 12 cm × 1.414 ≈ 16.97 cm
Therefore, the length of the hypotenuse is approximately 16.97 cm.