Question

in triangle nql, point s is the centroid, ns = (x + 10) feet, and sr = (x + 3) feet. what is rs? 4 feet 7 feet 10 feet 14 feet

Explanation:

Step1: Apply centroid segment ratio

The centroid divides a median into a 2:1 ratio, so $NS = 2 \times SR$.
Substitute the given expressions:
$x + 10 = 2(x + 3)$

Step2: Solve for x

Expand and simplify the equation:
$x + 10 = 2x + 6$
$10 - 6 = 2x - x$
$x = 4$

Step3: Calculate RS

Substitute $x=4$ into $SR = x + 3$:
$SR = 4 + 3$

Answer:

B. 7 feet