Use the relationships in 45-45-90 triangles to solve the following problem. If the hypotenuse of a triangle is 4 cm, what is the length of the leg?(1 point)

Answer 1

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of each leg.

Let x be the length of each leg.
The hypotenuse is 4 cm, so we have the equation 4 = √2x.
Squaring both sides of the equation, we get 16 = 2x^2.
Dividing both sides by 2, we get 8 = x^2.
Taking the square root of both sides, we get x ≈ √8.
Approximating √8 to the nearest cm, we get x ≈ 2.83.
Therefore, the length of each leg is approximately 2.83 cm. Answer: \boxed{2.83}.