The  length of the sides are given by the 45°–45°–90° triangle theorem.
Correct responses:
Methods used to find the lengths
The 45°–45°–90° triangle theorem states that the ratio of the lengths of
the sides of triangles having interior angles of 45°, 45°, 90° is 1 : 1 : √2
The lengths of the legs of an isosceles triangle are equal.
The legs of the given isosceles right triangle are AB and AC
Therefore;
AB = AC
Taking the lengths of AB as 1 unit, we have;
AB = 1 = AC
According to Pythagorean theorem, we have;
[tex]\overline{BC}^2 = \mathbf{\overline{AB}^2 + \overline{AC}^2}[/tex]
Which gives;
[tex]\overline{BC}^2 = 1^2 + 1^2 = \mathbf{ 2}[/tex]
Therefore;
BC = √2
Therefore, by setting the length of AB = AC = 1, we have;
The above values are in the ratio 1 : 1 : √2, which corresponds with the
45°-45°-90° triangle theorem.
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