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√2 cm
4 cm
4√2 cm

Explanation:

Step1: Recall ratio for 45 - 45 - 90 triangle

In a 45 - 45 - 90 triangle, the ratio of the length of a leg to the hypotenuse is $1:\sqrt{2}$. Let the length of each leg be $x$ and the hypotenuse be $c$. Then $c = x\sqrt{2}$.

Step2: Solve for the leg length

We know $c = 4$ cm. From $c=x\sqrt{2}$, we can solve for $x$ by dividing both sides of the equation by $\sqrt{2}$. So $x=\frac{4}{\sqrt{2}}$. Rationalize the denominator: $x=\frac{4\sqrt{2}}{2}=2\sqrt{2}$ cm.

Answer:

$2\sqrt{2}$ cm (corresponding to the option $2\sqrt{2}$ cm which is likely the second option in the multiple - choice list you provided, though the formatting of the options in the image is a bit unclear)