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2. The area of an isosceles...

Jonathan EvansJonathan Evans PowerScore StaffJoined: 10/31/2016

Description

  • Type: Quantitative Comparison
  • Topic: Geometry
    • Special Triangles
    • Draw a Figure
  • Answer: A, Quantity A is greater

Explanation


Consider scratch work above.
  1. Start by Recording What You Know™, drawing figures, and getting your Possibility Matrix™ and answer choices set up.
  2. Write any equations you will need, in this case the area of a triangle equation.
  3. An isosceles right triangle with two sides equal to 2 will have 2 as both the base and height. 
  4. Thus, we can calculate the value of column A (in blue): 2
  5. An equilateral right triangle with sides equal to 2 will have a base of 2, but we have to determine the height.
  6. Drop a line down from the vertex of the top angle. 
  7. This line bisects the base and forms a 30:60:90 special right triangle.
  8. Note the ratios of the sides of a 30:60:90 right triangle (in green).
  9. Use the values of this equilateral triangle to determine the height. a = 1, a­­√3 = √3
  10. The height of the equilateral triangle (in red) is √3.
  11. Thus, the area of this triangle is √3.
  12. √3 ≈ 1.7
  13. Column A is greater.
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