use a relationships in 45-45-90 triangles to solve the following problem. if the hypotenuse of a triangle is 4cm, what is the length of the leg?
In a 45-45-90 triangle, the length of each leg is equal. Let's assume the length of one leg as "x" cm.
Using the relationship in a 45-45-90 triangle, the hypotenuse is equal to √2 times the length of each leg. Therefore, we can set up the following equation:
√2 * x = 4 cm
To solve for x, we need to isolate it. Divide both sides of the equation by √2:
x = 4 cm / √2
To rationalize the denominator, multiply both the numerator and denominator by the conjugate of √2, which is √2:
x = (4 cm / √2) * (√2 / √2)
x = (4√2 cm) / 2
x = 2√2 cm
Therefore, the length of the leg is 2√2 cm.