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: Recall centroid property

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

Step2: Set up the equation

Since $NS=(x + 10)$ and $SR=(x + 3)$, we have the equation $x + 10=2(x + 3)$.

Step3: Solve the equation

Expand the right - hand side: $x + 10=2x+6$.
Subtract $x$ from both sides: $10=x + 6$.
Subtract 6 from both sides: $x=4$.

Step4: Find the length of $RS$

Substitute $x = 4$ into the expression for $SR$ (which is the same as $RS$). $RS=x + 3$.
So, $RS=4 + 3=7$ feet.

Answer:

7 feet