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Mathematics in grade two of junior high school 1. The opposite sides of two similar polygons are 3 cm and 4.5 cm respectively. If the sum of their areas is 130 square cm, then the area of the smaller polygon is 1________ square centimetre. 2. Given △ ABC ∽ a'b'c ', and ab: a'B' = 2:3, s △ ABC + s △ a'b'c '= 75, then s △ a'b'c'=______ .
Answer: 1:40 square centimeter; 2:675 / 13
The way to solve the problem: the way to solve the two questions is the same. They are all calculated according to "the area ratio of the similar polygon equals to the square of the similar ratio" (the area ratio of the similar triangle equals to the square of the similar ratio)
Let the area of the smaller polygon be X
Square of 3 / square of 4.5 = x / (130-x)
The solution is x = 40 square centimeter
Let the area of △ a'b'c 'be X
Square of 2 / square of 3 = (75-x) / X
The solution is x = 675 / 13 (or x = 51.92)
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