A potential deal has come up for a one-time sale of 32 units at a special price of $120 per unit. The marketing manager states that the sale will not negatively impact the company's regular sales activities and will require the normal variable manufacturing costs and selling and administrative costs. The production manager states that there is plenty of excess capacity and the deal will not impact fixed costs. The controller points out, however, that because the expected increase in revenues are equal to the expected increase in costs to fill the order, the deal will not have any impact on the bottom line.

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.

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