SAT Math Multiple Choice Practice Question 115: Answer and Explanation

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Question: 115


In the drawing above, line segment XY is parallel to line segment AB. If AB = 10, XY = 6, and the area of triangle ABC is 50, then the area of triangle XYC is

A. 18
B. 24
C. 30
D. 36
E. 44

Correct Answer: A


A. The rule in this case says that if two figures are similar, the ratio of their areas is the square of the ratios of their sides. This rule holds true for any two-dimensional figure, whether it's a triangle, a circle, or whatever. Because the ratio of the sides is 6:10, the ratio of the areas must be 36:100, and 36/100 × 50 = 18.

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