Question

the hypotenuse of a 45 - 45 - 90 triangle measures 18 cm. what is the length of one leg of the triangle? 9 cm 9\sqrt{2} cm 18 cm 18\sqrt{2} cm

Explanation:

Step1: Recall the ratio for 45 - 45 - 90 triangle

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

Step2: Solve for the leg length

We know $c = 18$ cm. From $c=a\sqrt{2}$, we can solve for $a$ by rearranging the formula: $a=\frac{c}{\sqrt{2}}$. Rationalize the denominator: $a=\frac{18}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{18\sqrt{2}}{2}=9\sqrt{2}$ cm.

Answer:

B. $9\sqrt{2}$ cm