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

the length of one leg of the triangle is, 7 units

Explanation:

Definition: 45°-45°-90°

In a 45°-45°-90° triangle, the length of one leg of the triangle is
`(1)/(√(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√(2)` units.

By definition of 45°-45°-90° ;

`x =(1)/(√(2)) \cdot \text{Length of hypotenuse side}`

Substitute the given values we have;

`x = (7√(2))/(√(2))`

Simplify:

`x = 7` units

Therefore, the length of one leg of the triangle is, 7 units