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 property

The centroid of a triangle divides each median into a ratio of \(2:1\), so \(NS = 2 \times QS\).

Step2: Set up equation

Substitute \(NS = 4x\) and \(QS = 3x - 5\) into the ratio: \(4x = 2(3x - 5)\).

Step3: Solve for x

Expand the right side: \(4x = 6x - 10\).
Subtract \(4x\) from both sides: \(0 = 2x - 10\).
Add 10 to both sides: \(2x = 10\).
Divide by 2: \(x = 5\).

Step4: Find NS

Substitute \(x = 5\) into \(NS = 4x\): \(NS = 4(5) = 20\) cm.

Answer:

20 cm