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?
In a 45-45-90 triangle, the two legs are congruent, which means they have the same length.
Let's represent the length of the leg as "x".
According to the relationships in a 45-45-90 triangle:
- The length of each leg is equal to x.
- 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:
√2 * x = 4 cm
To solve for x, divide both sides of the equation by √2:
x = 4 cm / √2
To rationalize the denominator, multiply the numerator and denominator by √2:
x = 4 cm / √2 * √2 / √2
Simplifying the expression, we have:
x = 4√2 cm / 2
x = 2√2 cm
Therefore, the length of the leg is 2√2 cm.