On February 1, 2019, Stephen (who is single) sold his principal residence (home 1) at a $100,000 gain. He was able to exclude the entire gain on his 2019 tax return. Stephen purchased and moved into home 2 on the same day. Assuming Stephen lives in home 2 as his principal residence until he sells it, which of the following statements is true? A. Under no circumstance will Stephen be allowed to exclude gain on home 2 if he sells home 2 in 2020.
B. Stephen will be eligible to exclude gain on home 2 only if he waits until 2024 to sell it.
C. In certain circumstances, Stephen may be able to exclude gain on home 2 even if he sells home 2 in 2019.
D. None of the choices are correct.

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.