Question

(20 points!) In triangle RSW, line segment RW is a median and is equal to 27 cm. What is the length of RX?

Answer 1

Answer:

Option D. 18 cm

Step-by-step explanation:

we know that

A centroid of a triangle is the point where the three medians of the triangle meet.

A median of a triangle is a line segment from one vertex to the mid point on the opposite side of the triangle.

The centroid divides each median in a ratio of 2:1

In this problem the centroid of triangle RST is the point X

so

$\frac{RX}{XW}=\frac{2}{1}$

$RX=2XW$ -----> equation A

$RX+XW=27$ -----> equation B

substitute equation A in equation B

$2XW+XW=27$

Solve for XW

$3XW=27$

$XW=9\ cm$

Find the value of RX

$RX=2XW$  ----- $RX=2(9)=18\ cm$