Question

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 30 cm

Explanation:

Step1: Recall centroid segment ratio

A centroid divides a median into a 2:1 ratio, so the longer segment (NS) is twice the shorter segment (QS).

Step2: Set up equation for x

$$4x = 2(3x - 5)$$

Step3: Solve for x

$$4x = 6x - 10$$
$$10 = 6x - 4x$$
$$10 = 2x$$
$$x = 5$$

Step4: Calculate NS

Substitute $x=5$ into $NS=4x$.
$$NS = 4 \times 5$$

Answer:

C. 20 cm