silemus.
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  1. 1Solving 4x−7=2x+9
  2. 2Linear cost equation
  3. 3System of two equations
  4. 4No solution, linear system
  5. 5Infinite solutions, linear system
  6. 6Weight limit word problem
  7. 7Solving a linear inequality
  8. 8Rate of change, cost per hour
  9. 9Finding slope then extending line
  10. 10Percent increase then decrease
  11. 11Percent: part is 18% of what
  12. 12Ratio split of 66 members
  13. 13Converting mph to ft/s
  14. 14Printer rate word problem
  15. 15Probability from a table
  16. 16Fraction from a table
  17. 17Mean shift, finding new value
  18. 18Median from a frequency table
  19. 19Factoring a quadratic
  20. 20Sum of roots, quadratic
  21. 21Vertex form of a parabola
  22. 22One solution, discriminant=0
  23. 23Max height of a parabola
  24. 24Percent growth rate, 1.03^t
  25. 25Exponential decay, 15% off
  26. 26Exponential growth, doubling
  27. 27Evaluating f(−2)
  28. 28Finding a, then g(-2)
  29. 29Composing f and g
  30. 30Shifting a graph f(x−3)+1
  31. 31Circle by completing the square
  32. 32Radius from two points
  33. 33Arc length from central angle
  34. 34Complementary angles in a triangle
  35. 35Tangent in a right triangle
  36. 36Isosceles right triangle area
  37. 37Similar triangles ratio
  38. 38Volume of a cylinder
  39. 39Volume of a sphere
  40. 40Scaling a box's volume
  41. 41Supplementary angles equation
  42. 42Setting up a cost equation
  43. 43Slope between two points
  44. 44x-intercept of a line
  45. 45Slope of perpendicular line
  46. 46Solving a linear system
  47. 47Two-ticket system of equations
  48. 48Solving a fraction equation
  49. 49Solving 7-3x>2x-18
  50. 50Height when planted, w=0
  51. 51No solution, linear equation
  52. 52Taxi cost inequality
  53. 53Intersecting lines, find k
  54. 54System of two equations
  55. 55Scaling 9x-6y+5
  56. 56Costly text message inequality
  57. 57Product of roots
  58. 58Matching exponent bases
  59. 59Solving a square root equation
  60. 60Equation with same denominator
  61. 61Vertex of a parabola
  62. 62Factor theorem on a cubic
  63. 63Exponential decay, halving
  64. 64Percent growth per year
  65. 65Solving f(a)=21 for a quadratic
  66. 66x²+y² from sum and product
  67. 67Sum of roots of intersection
  68. 68Exponential growth, V=2500(1.04)^t
  69. 69Composing g(x)=f(x+2)-3
  70. 70Completing the square
  71. 71Price per ounce comparison
  72. 72Percent increase
  73. 73Percent off, then tax
  74. 74Mean with a score removed
  75. 75Overlapping sets, neither
  76. 76Map scale ratio problem
  77. 77Converting rate units
  78. 78Line of best fit
  79. 79Median of a data set
  80. 80Scaling up a sample
  81. 81Percent of a percent
  82. 82Average speed, unequal times
  83. 83Ratio of flour to sugar
  84. 84Two successive percent decreases
  85. 85Fraction of a subgroup
  86. 86Mixing to a target percent
  87. 87Triangle angle sum
  88. 88Ladder as right triangle
  89. 89Area of a trapezoid
  90. 9030-60-90 triangle sides
  91. 91Area of a circle sector
  92. 92Inscribed angle theorem
  93. 93Circle from diameter endpoints
  94. 94Volume of a cone
  95. 95Cube volume to surface area
  96. 96Sine-cosine complementary angles
  97. 97Area ratio of similar triangles
  98. 98Diagonal of a rectangle
  99. 99Same-side interior angles
  100. 100Right triangle, tan from cos
  101. 101Volume displaced raises water

97Area ratio of similar triangles

Triangle ABC is similar to triangle DEF, where AB corresponds to DE. AB = 4, DE = 10 and the area of triangle ABC is 12. What is the area of triangle DEF?

The area of triangle DEF is 75. Similar triangles scale sides by one factor, here k = DE/AB = 10/4 = 5/2, but area scales by k², so Area(DEF) = 12 × (25/4) = 75.

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