Missing lengths of a 45°-45°-90° Special Right Triangle given Hypotenuse length = √24 = 2√6 (simplified)

Leg lengths of a 45°-45°-90° Special Right Triangle are equal
Leg lengths =
Hypotenuse length/√2

Leg lengths =
2√6/√2

Since 6 is divisible by 2, apply the quotient rule for radicals:
Leg lengths =
2√6/√2
= 2
√
6/2

Leg lengths = 2√3 = 3.464101615138

The solution above and all other related solutions were provided by the 45°-45°-90° Special Right Triangle Application. 

Find Missing Lengths of a 45-45-90 Special Right Triangle

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