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Unformatted text preview: ncludes the ratios of corresponding sides, medians, altitudes, angle bisectors, radii, diameters, perimeters, and circumferences. The ratio is referred to as the linear ratio or ratio of similitude. If triangle ABC is similar to triangle DEF and the segments are given as marked, then EH is equal to 2.5 because the linear ratio is 6 : 3 or 2 : 1. D. When figures are similar, the ratio of their areas is equal to the square of the linear ratio. If triangle ABC is similar to triangle DEF, the area of triangle ABC will be 9 times as great as the area of triangle DEF. The linear ratio is 12 : 4 or 3 : 1. The area ratio will be the square of this or 9 : 1. If the area of triangle ABC had been given as 27, the area of triangle DEF would be 3. www.petersons.com Geometry 221 E. When figures are similar, the ratio of their volumes is equal to the cube of their linear ratio. The volume of the larger cube is 8 times the volume of the smaller cube. The ratio of sides is 4 : 2 or 2 : 1. The ratio of areas would be 4 : 1. The ratio of volumes would be 8 : 1. Exercise 10
Work out each problem. Circle the letter that appears before your answer. 1. If the area of a circle of radius x is 5π, find the area of a circle of radius 3x. (A) 10π (B) 15π (C) 20π (D) 30π (E) 45π If the length and width of a rectangle are each doubled, the area is increased by (A) 50% (B) 100% (C) 200% (D) 300% (E) 400% The area of one circle is 9 times as great as the area of another. If the radius of the smaller circle is 3, find the radius of the larger circle. (A) 9 (B) 12 (C) 18 (D) 24 (E) 27 4. If the radius of a circle is doubled, then (A) the circumference and area are both doubled (B) the circumference is doubled and the area is multiplied by 4 (C) the circumference is multiplied by 4 and the area is doubled (D) the circumference and area are each multiplied by 4 (E) the circumference stays the same and the area is doubled The volumes of two similar solids are 250 and 128. If a dimension of the larger solid is 25, find the corresponding side of the smaller solid. (A) 12.8 (B) 15 (C) 20 (D) 40 (E) cannot be determined 2. 5. 3. www.petersons.com 222 Chapter 13 RETEST
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 Spring '10
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