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 \(1:1:\sqrt{2}\)
then,
the measures of the sides are \(x , x ,\sqrt{2}x\)
The length of hypotenuse= \(\sqrt{2}\) times the length of the leg. ....[1]
Given: length of hypotenuse = 128 cm.
then,
from [1] we have;
128 = \(\sqrt{2}\cdot x\)
or
\(x=\frac{128}{\sqrt{2}}\) = \(\frac{128}{\sqrt{2} } \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{128\sqrt{2}}{\sqrt{2}\cdot \sqrt{2}}\)
Simplify:
\(x =\frac{128 \cdot \sqrt{2}}{2} =64\sqrt{2}\) cm.
Therefore, the length of one leg of the triangle is; \(64\sqrt{2}\) cm.
