Question

In triangle nql, point s is the centroid, ns = (x + 10) feet, and sr = (x + 3) feet. Triangle n q l has centroid s. Lines are drawn from each point to the midpoint of the opposite side to form line segments n r, q m, and l p. The length of line segment n s is x + 10 and the length of line segment s r is x + 3. What is rs?.

Answer 1

Answer: Answer:

B. 7 feet

Explanation:

Given:

NS = (x + 10) ft

SR = (x + 3) ft

Required:

RS

SOLUTION:

Based in the centroid theorem, the centroid, S will divide the median, line segment NR, into NS and SR, such that NS : SR = 2 : 1.

Therefore:

NS = 2(SR)

x + 10 = 2(x + 3) (substitution)

Solve for x

x + 10 = 2x + 6

Collect like terms

x - 2x = -10 + 6

-x = -4

divide both sides by -1

x = 4

SR = (x + 3) ft (SR is same as RS)

Plug in the value of x

SR = (4 + 3) ft

SR = RS = 7 ft