Question

Triangle L N P has centroid S. Lines are drawn from each point to the midpoint of the opposite side to form line segments N R, L P, and Q M. The length of line segment N S is 7 x minus 3 and the length of line segment S R is 5 x minus 3. What is the length of segment NS? 1 unit 2 units 4 units 6 units

Answer 1

Answer:

6 units

Step-by-step explanation:

Given: Triangle L N P has centroid S.

$NS=7x-3, SR=5x-3$

To find: NS

Solution:

Centroid is the point of intersection of the medians of the triangle such that it divides each of the median in ratio $2:1$

So,

$NS:SR=2:1\\\frac{NS}{SR}=\frac{2}{1}$

Put $NS=7x-3, SR=5x-3$

$\frac{7x-3}{5x-3}=\frac{2}{1}\\ 7x-3=10x-6\\10x-7x=-3+6\\3x=3\\x=1$

Therefore,

$NS=7x-3=7(1)-3=4\,\,units\\SR=5x-3=5(1)-3=2\,units$

So,

$NS=NS+SR=4+2=6\,\,units$

Answer 2

Answer:

The answer is 4

Step-by-step explanation:

It asks for the length of NS not the length of NR