Question

The hypotenuse of a 45°-45°-90° triangle measures 22 2 units.

What is the length of one leg of the triangle

11 units
11^2 units
22 units
22^2 units

Answer 1

The Answer Is:

C) 22 units

Answer 2

Option C.

Explanation:

Given information: The hypotenuse of a 45°-45°-90° triangle measures 22√2 units.

Let x be the length of one leg.

From the given figure it is clear that length of both legs are same.

According to the Pythagoras theorem, in a right angled triangle

`(leg_1)^2+(leg_2)^2=hypotenuse^2`

Substitute
`leg_1=leg_2=x, hypotenuse=22√(2)` in the above formula.

`(x)^2+(x)^2=(22√(2))^2`

`2x^2=(22)^2(√(2))^2`

`2x^2=2(22)^2`

Divide both sides by 2.

`x^2=(22)^2`

Taking square root on both sides.

`x=22`

The length of one leg is 22 units.

Therefore, the correct option is C.