in triangle nlm, point s is the centroid, qs = (3x - 5) cm, and ns = (4x) cm. what is ns? 5 cm 10 cm 20 cm…

Explanation:

Step1: Recall centroid property

The centroid of a triangle divides each median in a 2:1 ratio. So, $NS = 2QS$.

Step2: Set up the equation

Substitute the given expressions: $4x=2(3x - 5)$.

Step3: Solve the equation

Expand the right - hand side: $4x = 6x-10$. Then, move the $x$ terms to one side: $6x - 4x=10$, which simplifies to $2x = 10$. Divide both sides by 2: $x = 5$.

Step4: Find NS

Substitute $x = 5$ into the expression for $NS$. Since $NS = 4x$, then $NS=4\times5=20$ cm.

Answer:

20 cm