Question

the hypotenuse of a 45-45-90 triangle has a length of 10 units. what is the length of one of its legs?

a. $10\sqrt{2}$ units

b. 5 units

c. 10 units

d. $5\sqrt{2}$ units

Explanation:

Step1: Define variables for legs

Let each leg length be $x$ (since 45-45-90 triangles have equal legs).

Step2: Apply Pythagorean theorem

$$x^2 + x^2 = 10^2$$

Step3: Simplify the equation

$$2x^2 = 100$$
$$x^2 = 50$$

Step4: Solve for $x$

$$x = \sqrt{50} = 5\sqrt{2}$$

Answer:

D. $5\sqrt{2}$ units