the hypotenuse of a 45 - 45 - 90 triangle measures 18 cm. what is the length of one leg of the triangle? 9…
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
Answer
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 $c$, then $c = a\sqrt{2}$.
Step2: Solve for the leg length
Given $c = 18$, we have $18=a\sqrt{2}$. Solving for $a$, we get $a=\frac{18}{\sqrt{2}}$. Rationalize the denominator: $a=\frac{18\sqrt{2}}{2}=9\sqrt{2}$.
Answer:
B. $9\sqrt{2}$ cm