Math Geom Ch 6 Midterm Review Solutions

Midterm Review Chapter 6 Geometry CP Name: Key The perimeter and the ratio of length to width of a rectangle are given. Find the length and width of the rectangle. 1. Perimeter = 132 cm 1:w = 7:4 4x + 7x + 4x + 7x = 132 22x = 132 x = 6 l = 7x = 42 cm w = 4x = 24 cm 2. Perimeter = 280 ft 1:w = 11:9 9x + 11x + 9x + 11x = 280 40x = 280 x = 7 l = 11x = 77 ft w = 9x = 63 ft The measures of the angles of a triangle are in the extended ratio given. Find the measures of the angles of the triangle. 3. 3:7:10 3x + 7x + 10x = 180 20x = 180 x = 9 Angles: 27°, 63°, 90° 4. 7:16:22 7x + 16x + 22x = 180 45x = 180 x = 4 Angles: 28°, 64°, 88° Solve the following proportions. 5. x/16 = 24/12 12x = 384 x = 32 6. 3/11 = 27/x 3x = 297 x = 99 7. 20/(6x - 1) = 8/14 280 = 8(6x - 1) 35 = 6x - 1 36 = 6x x = 6 8. 19(15d - 11) = 32(7d + 3) 285d - 209 = 224d + 96 61d = 305 d = 5 Use the given ratio and information in the figure to find the value of the variable(s). 11. CD:AB = 5:3 5x = 195 x = 39 12. RS:RT = 13:25 104/(18z - 16) = 13/25 2600 = 13(18z - 16) 2600 = 234z - 208 2808 = 234z z = 12 Find the geometric mean of the following numbers. 13. 7 and 28 x² = 7 * 28 x² = 196 x = 14 14. 4 and 12 x² = 4 * 12 x² = 48 x = 4√3 15. 15 and 45 x² = 15 * 45 x² = 675 x = 15√3 Complete the statements below. 16. If a/b = x/y, then a/x = b/y 17. If 7/12 = 31/y, then 19/12 = 7y/31 18. If x/c = y/z, then c/y = x/z 19. If 3/4 = 5/(x+2), then 7/4 = 2(x+7)/(x+2) In the diagram, AB/CD = AG/FE and AB/AC = AG/AF. Find the unknown length. 20. Find AB AB = 30 x/18 = 35/21 21x = 630 x = 30 21. Find GF GF = 28 30/54 = 35/(y+35) 30(y+35) = 1890 30y + 1050 = 1890 30y = 840 y = 28 The length of a feature in a scale model is given along with the corresponding length of the actual object. Find the scale of the model.   22. Length in model: 6.5 inches; Actual length: 91 inches 6.5/91 = 1/14 1:14 23. Length in model: 26 centimeters; Actual length: 3.25 millimeters 26 cm * 10 mm/cm = 260 mm 260/3.25 = 80 80:1 Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor of Figure A to Figure B. 24. Yes, SSS.   ΔLMN ~ ΔPQR Scale factor = 4/3 25. Yes, SSS. ABCD ~ HEFG Scale factor = 5/8 In the diagram at the right, quadrilateral BCDE ~ WXYZ. 26. Find the scale factor of quad. BCDE to quad. WXYZ. 2/3 27. Find the scale factor of quad. WXYZ to quad. BCDE. 3/2 28. Find XY. XY = 4.5 29. Find m∠1. m∠1 = 117° 30. Find the perimeter of quad. WXYZ. P = 24 In the diagram, PQRS ~ WXYZ. 31. Find the scale factor of PQRS to WXYZ. 2/3 32. Find the values of x, y, and z. x = 8, y = 118, z = 15 Determine whether the two triangles are similar. If they are similar, write a similarity statement. 33. Yes, SAS. ΔDEF ~ ΔABC 34. Yes, AA. ΔQRS ~ ΔTSU Find all possible values for x in the similar triangles. 35. ΔFGH ~ ΔHKL (7 - x)(x² + 20) = (13 - x)(x² + 5) 0 = 4x² + 15x - 75 x = -15/4, 5 36. ΔPQR ~ ΔSTU (x + 2)(13 - x) = (x + 5)(7 - x) 0 = 4x² - 24x x = 0, 6