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?
2√2 cm
2√3 cm
4√2 cm
2 cm
In a 45-45-90 triangle, the length of the hypotenuse is equal to √2 times the length of each leg.
Given that the hypotenuse is 4 cm, we can set up the following equation:
4 cm = √2 * length of leg
To solve for the length of the leg, we divide both sides of the equation by √2:
length of leg = 4 cm / √2
To rationalize the denominator, we multiply both the numerator and denominator by √2:
length of leg = (4 cm / √2) * (√2 / √2)
Simplifying the expression gives us:
length of leg = (4 cm * √2) / 2
length of leg = 2√2 cm
Therefore, the length of the leg is 2√2 cm.