SAT Math Multiple Choice Question 56: Answer and Explanation

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Question: 56


In the figure above, what is the length of ?

  • A. 8
  • B. 9
  • C. 12
  • D. 15

Correct Answer: C


CThe 5 equal lengths that make up the two sides of the largest triangle tell us that we are dealing with 5 similar triangles. The largest triangle has sides 15:25:30, and the sides of all 5 triangles will have an equivalent ratio. Reduced, the ratio is 3:5:6, which happens to be the dimensions of the smallest triangle. We want to find the length of BD, the base of a triangle with sides of 6 and 10. This is twice as big as the smallest triangle, so the base BD must be 6 × 2 =12, which is (C).

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