A 45-45-90 triangle is an isosceles right triangle, and its sides have a specific ratio. In such triangles, the lengths of the legs are equal, and the hypotenuse is √2 times the length of a leg.
For example, if the lengths of the legs are both ‘x’, the length of the hypotenuse would be ‘x√2’. Therefore, if we consider potential lengths:
- If the legs are 1, then the hypotenuse is 1√2 (approximately 1.41).
- If the legs are 2, then the hypotenuse is 2√2 (approximately 2.83).
- If the legs are 3, then the hypotenuse is 3√2 (approximately 4.24).
Thus, the possible side lengths of a 45-45-90 triangle could be in the form of (x, x, x√2), where ‘x’ is any positive number. The important thing to remember is the ratio: the two legs must be equal, and the hypotenuse must be equal to the leg length multiplied by √2.