Question

In the diagram below of triangle B, C, DBCD, EE is the midpoint of start overline, B, D, end overline
BD
and FF is the midpoint of start overline, C, D, end overline
CD
. If E, F, equals, minus, 32, plus, 8, xEF=−32+8x, and B, C, equals, 6, x, minus, 4BC=6x−4, what is the measure of start overline, B, C, end overline
BC
?

Answer 1

E and F are midpoints of BD and CD, so EF is the midsegment parallel to BC and EF = (1/2)BC.

Set up the equation:
-32 + 8x = (1/2)(6x - 4)

Solve:
-32 + 8x = 3x - 2
5x = 30
x = 6

Then BC = 6x - 4 = 6(6) - 4 = 36 - 4 = 32.

Answer: BC = 32.