1. In the triangle RST, E is the midpoint of line RS and F is the midpoint of line ST. If EF= 8y – 3 and RT = 3y + 20, find y and the length of line EF and line RT.

Question

2. In a trapezoid BYTE, line BE̅ ∥ line YT and median LM is drawn.

If YT = x + 9, LM = x + 15, and BE = 2x – 5, find the length of lines YT, LM, and BE.

Answer 1

1) To solve this problem, you need to know the triangle midline theorem:

A line segment connecting the midpoints of two sides of a triangle will be parallel to the third side and have half of its length.

So, we have:

RT = 2·EF

3y + 20 = 2(8y - 6)

Solve for y, then plug that value of y into the equations for EF and RT to find their lengths.

2) To solve this problem, you need to know that in a trapezoid the median line (aka the midline), LM, is equal to the average of YT and BE:

LM = (YT + BE) / 2

Plug in the formulas for LM, YT, and BE then solve for y. Plug the value of y you get into the given formulas for LM, YT, and BE to find their lengths.