Question

the hypotenuse of a 45°-45°-90° triangle measures 4 cm. what is the length of one leg of the triangle?
○ 2 cm
○ $2\sqrt{2}$ cm
○ 4 cm
○ $4\sqrt{2}$ cm

Explanation:

Step1: Recall 45-45-90 triangle rule

In a 45-45-90 triangle, leg length $l = \frac{\text{hypotenuse}}{\sqrt{2}}$

Step2: Substitute hypotenuse value

Hypotenuse = 4 cm, so $l = \frac{4}{\sqrt{2}}$

Step3: Rationalize the denominator

$l = \frac{4}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{4\sqrt{2}}{2} = 2\sqrt{2}$

Answer:

$2\sqrt{2}$ cm (Option B)