Question

The hypotenuse of a 45°-45°-90° triangle measures 7√2 units. what is the length of one leg of the triangle

Answer 1

7 because a(one side)= 1/sqrt2 * hypotenuse (7*sqrt2) THis equals 7

Answer 2

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