Question

question 10 of 10
what is the length of leg s of the triangle below?
a. $sqrt{3}$
b. 1.7
c. 9
d. 3
e. 1.5
f. $sqrt{18}$

Explanation:

Step1: Identify triangle type

It's a 45 - 45- 90 right - triangle. In a 45 - 45- 90 triangle, the ratio of the sides is $1:1:\sqrt{2}$, where the legs are of equal length and the hypotenuse is $\sqrt{2}$ times the length of a leg. Let the length of each leg be $s$. The hypotenuse $c=\sqrt{18}$.

Step2: Apply the 45 - 45- 90 triangle formula

We know that $c = s\sqrt{2}$. Given $c=\sqrt{18}$, then $\sqrt{18}=s\sqrt{2}$.

Step3: Solve for $s$

First, simplify $\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}$. So, $3\sqrt{2}=s\sqrt{2}$. Divide both sides by $\sqrt{2}$: $s = 3$.

Answer:

D. 3