Question

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) 2√2 cm 4√2 cm 2 cm 2√3 cm

Explanation:

Step1: Recall the ratio of sides in a 45 - 45 - 90 triangle

In a 45 - 45 - 90 triangle, the ratio of the sides is \(1:1:\sqrt{2}\), where the legs are of equal length \(x\) and the hypotenuse is \(x\sqrt{2}\).

Step2: Set up the equation for the hypotenuse

Let the length of each leg be \(x\). Given the hypotenuse \(c = 4\) cm. Using the formula \(c=x\sqrt{2}\), we can solve for \(x\).

$$x=\frac{c}{\sqrt{2}}$$

Substitute \(c = 4\) into the equation:

$$x=\frac{4}{\sqrt{2}}$$

Step3: Rationalize the denominator

Multiply the numerator and denominator by \(\sqrt{2}\)

$$x=\frac{4\sqrt{2}}{2}=2\sqrt{2}$$

Answer:

\(2\sqrt{2}\text{ cm}\) (the first option)