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It is known that the perimeter of △ ABC is 18cm, and a + B = 2c, a − B = C2. Find the length of a, B, C on three sides
From the meaning of the title: a + B = 2ca − B = C2A + B + C = 18, the solution: a = 7.5B = 4.5c = 6 〉 A is 7.5cm long, B is 4.5cm long, C is 6cm long
The ratio of three sides of △ ABC is 3:4:6, △ a1b1c1 is similar to △ ABC. If the longest side of △ a1b1c1 is 18cm, find the perimeter of △ ABC!
Because △ a1b1c1 is similar to △ ABC,
At the same time, the ratio of three sides of △ ABC is 3:4:6
So the ratio of the three sides of △ a1b1c1 is 3:4:6
Because the longest side of △ a1b1c1 is 18cm
So the three sides of △ a1b1c1 are 9cm, 12cm and 18cm
The perimeter of △ a1b1c1 is 39cm
There is no fixed solution for the circumference of △ ABC
In △ ABC, ab = 6, BC = 10, CA = 8, connect the midpoint of △ ABC in turn to get △ a1b1c1, connect the midpoint of △ a1b1c1 in turn to get △ a2b2c2, and so on
(1) Find the perimeter and area of △ a2b2c2
(2) Find the perimeter and area of △ anbncn (n is a positive integer)
The perimeter of △ a2b2c2 is: (6 + 10 + 8) * 1 / 4 = 6
The area of △ a2b2c2 is: [(6 * 8) * 1 / 2] * 1 / 4 * 1 / 4 = 1.5
The perimeter of △ anbncn is: (6 + 10 + 8) * [(1 / 2) n power]
The area of △ a2b2c2 is: [(6 * 8) * 1 / 2] * [(1 / 4) n power]
As shown in the figure, take the three sides of triangle ABC as sides, and make three equilateral triangles on the same side of BC. What are the four sides of quadrilateral ADEF
Let the three equilateral triangles be △ abd △ ACF △ BCE to form a quadrilateral ADEF, then: the quadrilateral ADEF is a parallelogram according to the meaning: ∵ abd △ ACF △ BCE is an equilateral triangle ∵ AB = BD angle EBC = angle DBA = 60 ° be = BC ∵ angle DBE + angle EBA = angle ABC + angle EBA ∵ angle DBE = angle ABC and ∵ DB = ab
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