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 \(2:1\), with the longer segment being closer to the vertex. So, \(NS = 2 \times QS\).

Step2: Set up the equation

Given \(QS=(3x - 5)\) and \(NS = 4x\), using the centroid property:
\(4x=2(3x - 5)\)

Step3: Solve for \(x\)

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

Step4: Find \(NS\)

Substitute \(x = 5\) into \(NS = 4x\):
\(NS=4\times5=20\)

Answer:

20 cm