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1、Ratios But I can set up the proportion in the exact same way: Now Ill solve for x: (3)(12) = x2 36 = x2 Since I cant take the square root of a negative number, then there is no solution for the mean proportion of the two given values.,Find the unknown value in the proportion: (2x + 1) : 2 = (x + 2)
2、: 5 (2x + 1) : 2 = (x + 2) : 5 First, I convert the ratios to fractional form: Then I solve the proportion:5(2x + 1) = 2(x + 2) 10 x + 5 = 2x + 4 8x = 1 x = -1/8,Another proportion problem is that of similar figures. Similar is a geometric term, referring to geometric shapes that are the same, excep
3、t that one is larger than the other. If youve used a graphics program, think aspect ratio.,The pairs of corresponding sides are proportional. That is, A : a = B : b = C : c. This proportionality of corresponding sides can be used to find the length of a side of a figure.,The “corresponding sides” ar
4、e the pairs of sides that “match”, except for the enlargement / reduction aspect of their relative sizes. So A corresponds to a, B corresponds to b, and C corresponds to c.,In the displayed triangles, the lengths of the sides are given by A = 48 mm, B = 81 mm, C = 68 mm, and a = 21 mm. Find the leng
5、ths of sides b and c, rounded to the nearest whole number. b 48 = 21 8148b = 1701 b = 35.4375 c 48 = 21 6848c = 1428 c = 29.75,Finding the height of something very tall by using the daytime shadow length of that same thing, its shadow being down along the ground, and thus easily measurable.,The sun
6、is far enough away that the rays of light that reach one general area on the planet may safely be regarded as being parallel. This obviously would not be the case for a nearby light-source, such as a helicoptor hovering overhead.,A building casts a 103-foot shadow at the same time that a 32-foot fla
7、gpole casts as 34.5-foot shadow. How tall is the building?,34.5 h = 103 3234.5h = 3296 h = 95.5362318841.,I first draw the building, the flagpole, a line for the (flat) ground, and the lines indicating the sunlights path: This gives me two similar (and right) triangles.,The famous ancient Greek temp
8、le, the Parthenon, in the Acropolis in Athens, Greece.,The golden proportion (1 : 1.618 = 0.618 : 1) appeared in many of the proportions of the Parthenon.,The ancient Egyptian Pyramid also has many data associated with 0.618.,The human body having leg length and height ratio of 0.618:1 is most beautiful.,Stringed instrument bridge on the 0.618 point can make the music more soft and sweet.,The length and width ratio of LCD TV is abo
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