Question

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Find the length of the hypotenuse of an isosceles right triangle whose legs are 1 unit in length.

Answer 1

Pythagoras theorem

`{x}^(2) = {1}^(2) + {1}^(2) \\ {x}^(2) = 1 + 1 \\ {x}^(2) = 2 \\ x = √(2) = 1.41`

Answer 2

The length of the hypotenuse of the isosceles right triangle with leg of length unit is:

√2 units.

Explanation:

Let a and b denote the leg of a right triangle and c denote the hypotenuse of the right triangle.

Now we apply the Pythagorean Theorem as:

`c^2=a^2+b^2`

Now as triangle is isosceles.

Hence, a=b=1 unit

`c^2=1^2+1^2\\\\c^2=2\\\\c=√(2)`

Hence, the length of the hypotenuse is:

√2 units.