i need to figure out side lengths of congruent right isosceles triangle with no lengths given. I know that the hypotenese is 1 per pythogoras constant and the area is a^2/2. I don't have to prove area just side lengths.
To find the side lengths of a congruent right isosceles triangle, we can use the Pythagorean theorem and the knowledge that the hypotenuse is equal to 1 (per Pythagoras constant).
Let's denote the length of each side of the triangle as 's'. Since it is a right isosceles triangle, two sides will have length 's' and the remaining side, the hypotenuse, will have length 1.
Using the Pythagorean theorem, we have:
s^2 + s^2 = 1^2
Simplifying the equation:
2s^2 = 1
Dividing both sides by 2, we get:
s^2 = 1/2
To find the side length 's', we take the square root of both sides:
s = √(1/2)
Now, simplifying the square root:
s = √(1) / √(2)
Since the square root of 1 is 1:
s = 1 / √(2)
To rationalize the denominator, we multiply the numerator and denominator by the conjugate of √(2) which is also √(2):
s = (1 / √(2)) * (√(2) / √(2))
Multiplying the numerators and denominators, we get:
s = √(2) / (2)
So, the side length of the congruent right isosceles triangle is √(2) / (2).
Please note that this calculation assumes that the triangle is scaled such that its hypotenuse is equal to 1.