Question

special right triangles #3
unique id: 1080
this is the only question in this section.
question
solve for k.
answer attempt 1 out of 3
k =

Explanation:

Step1: Identify triangle type

This is a 45 - 45- 90 special 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 $c$ is $\sqrt{2}$ times the length of a leg $a$ (i.e., $c = a\sqrt{2}$).

Step2: Determine side relationship

The given leg length is $3\sqrt{5}$. Let the length of the other leg be $w$ and the hypotenuse be $k$. In a 45 - 45- 90 triangle, if one leg $a = 3\sqrt{5}$, and the hypotenuse $k$ and leg $a$ are related by $k=a\sqrt{2}$.

Step3: Calculate $k$

Substitute $a = 3\sqrt{5}$ into the formula $k=a\sqrt{2}$. Then $k=3\sqrt{5}\times\sqrt{2}=3\sqrt{10}$.

Answer:

$3\sqrt{10}$