The hypotenuse of a 45°-45°-90° triangle measures 7√2 units. what is the length of one leg of the triangle
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 \(\frac{1}{\sqrt{2}}\) 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
⇒\(\text{Length of Hypotenuse side} = 7\sqrt{2}\) units.
By definition of 45°-45°-90° ;
\(x =\frac{1}{\sqrt{2}} \cdot \text{Length of hypotenuse side}\)
Substitute the given values we have;
\(x = \frac{7\sqrt{2}}{\sqrt{2}}\)
Simplify:
\(x = 7\) units
Therefore, the length of one leg of the triangle is, 7 units