Mankus inc. is considering using stocks of an old raw material in a special project. the special project would require all 180 kilograms of the raw material that are in stock and that originally cost the company $2,406 in total. if the company were to buy new supplies of this raw material on the open market, it would cost $7.05 per kilogram. however, the company has no other use for this raw material and would sell it at the discounted price of $6.35 per kilogram if it were not used in the special project. the sale of the raw material would involve delivery to the purchaser at a total cost of $68 for all 180 kilograms. what is the relevant cost of the 180 kilograms of the raw material when deciding whether to proceed with the special project?

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.