On March 31, 2021, the Herzog Company purchased a factory complete with vehicles and equipment. The allocation of the total purchase price of $1,000,000 to the various types of assets along with estimated useful lives and residual values are as follows: Asset Cost Estimated Residual Value Estimated Useful Life (in Years) Land $ 100,000 N/A N/A Building 500,000 none 25 Equipment 240,000 10% of cost 8 Vehicles 160,000 $ 12,000 8 Total $ 1,000,000 On June 29, 2022, equipment included in the March 31, 2021, purchase that cost $100,000 was sold for $80,000. Herzog uses the straight-line depreciation method for buildings and equipment and the double-declining-balance method for vehicles. Partial-year depreciation is calculated based on the number of months an asset is in service.

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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