Respuesta :
Answer:
the length of one leg of the triangle is, 7 units
Step-by-step explanation:
Definition: 45°-45°-90°
In a 45°-45°-90° triangle, the length of one leg of the triangle is [tex]\frac{1}{\sqrt{2}}[/tex] times the length of Hypotenuse of the triangle.
Let x be the length of one leg of the triangle.
As per the statement:
The hypotenuse of a 45°-45°-90° triangle measures 7√2 units
⇒[tex]\text{Length of Hypotenuse side} = 7\sqrt{2}[/tex] units.
By definition of 45°-45°-90° ;
[tex]x =\frac{1}{\sqrt{2}} \cdot \text{Length of hypotenuse side}[/tex]
Substitute the given values we have;
[tex]x = \frac{7\sqrt{2}}{\sqrt{2}}[/tex]
Simplify:
[tex]x = 7[/tex] units
Therefore, the length of one leg of the triangle is, 7 units
