Answer:
Since, a 45°-45°-90° triangle is a special type of isosceles right triangle, where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.
In 45°−45°−90° triangle
Sides are in the proportion [tex]1:1:\sqrt{2}[/tex]
then,
the measures of the sides are [tex]x , x ,\sqrt{2}x[/tex]
The length of hypotenuse= [tex]\sqrt{2}[/tex] times the length of the leg. ....[1]
Given: length of hypotenuse = 128 cm.
then,
from [1] we have;
128 = [tex]\sqrt{2}\cdot x[/tex]
or
[tex]x=\frac{128}{\sqrt{2}}[/tex] = [tex]\frac{128}{\sqrt{2} } \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{128\sqrt{2}}{\sqrt{2}\cdot \sqrt{2}}[/tex]
Simplify:
[tex]x =\frac{128 \cdot \sqrt{2}}{2} =64\sqrt{2}[/tex] cm.
Therefore, the length of one leg of the triangle is; [tex]64\sqrt{2}[/tex] cm.
