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 the ratio of sides

In a 45 - 45 - 90 triangle, if the length of each leg is $a$ and the hypotenuse is $c$, the ratio of the sides is $a:a:c = 1:1:\sqrt{2}$, so $c = a\sqrt{2}$.

Step2: Solve for the leg length

Given $c = 4$ cm, and $c=a\sqrt{2}$, we can solve for $a$ by rearranging the formula: $a=\frac{c}{\sqrt{2}}$. Substitute $c = 4$ into the formula: $a=\frac{4}{\sqrt{2}}$. Rationalize the denominator: $a=\frac{4\sqrt{2}}{2}=2\sqrt{2}$ cm.

Answer:

B. $2\sqrt{2}$ cm