The side ratio of a 45-45-90 triangle is …
1 : 1 : √2
The side ratio of a 45-45-90 triangle is x:x:x√2, where x is the length of the two legs, and x√2 is the length of the hypotenuse. This means that the two legs of the triangle are congruent, and the length of each leg is equal to x. The hypotenuse of the triangle is the side opposite the right angle, and its length is x√2.
To illustrate, if one leg of a 45-45-90 triangle has a length of 4 units, then the other leg will also have a length of 4 units. The hypotenuse is calculated by multiplying the length of one leg by the square root of 2. Therefore, the hypotenuse in this case will be 4√2 units long.
This side ratio property is useful in solving problems involving 45-45-90 triangles. For instance, if we know the length of one side of the triangle, we can easily find the length of the other sides using this ratio.
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