Find the length of the hypotenuse of an isosceles right triangle whose legs are 1 unit in length.
H^2 = 1^2 + 1^2
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H = ....
To find the length of the hypotenuse of an isosceles right triangle, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's call the length of the legs of the triangle "a" and the length of the hypotenuse "c". In this case, both legs are 1 unit in length, so a = 1.
The Pythagorean theorem can be written as:
c^2 = a^2 + a^2
c^2 = 1^2 + 1^2
c^2 = 1 + 1
c^2 = 2
To find the length of the hypotenuse, we take the square root of both sides:
c = √2
So, the length of the hypotenuse of the isosceles right triangle with legs of 1 unit in length is √2 (approximately 1.414 units).