F.1 maths algebraic
2012-07-30 11:23 pm
in the figure, an equilateral triangle is cut into 9 equal equilateral triangles.if the total perimeter of the 9 small triangles is 54 cm more than the perimeter of the original triangle, find the length of a side of the original triangle
回答 (2)
2012-07-31 3:16 am
✔ 最佳答案
The original triangle can be divided to be this figure:top:1 triangle
middle:3 triangle
base:5 triangle
Therefore,every lengths of the original triangle will be divided by 3
Let every length of the original triangle be x
3x+54=9[3(x/3)]
54=9x-3x
54=6x
x=9 cm
Therefore, the length of a side of the original triangle is 9cm
參考: me
2012-07-31 3:46 am
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....../__\ /__\
..../\..../ \..../\
../__\ /__\ /__\
The triangle should be divided like this.
[Please ignore the dots.]
(Hope you can understand the figure.)
The perimeter of the 9 small triangles is 54cm.
Therefore, the side of 1 triangle is: 54 ÷ 9 ÷ 3 = 2cm.
Hence, the side of the original triangle is: 2 × 3 = 6cm.
(According to the figure, the side of the original triangle is 3 times of a small
triangle.)
........../__\
......../\..../\
....../__\ /__\
..../\..../ \..../\
../__\ /__\ /__\
The triangle should be divided like this.
[Please ignore the dots.]
(Hope you can understand the figure.)
The perimeter of the 9 small triangles is 54cm.
Therefore, the side of 1 triangle is: 54 ÷ 9 ÷ 3 = 2cm.
Hence, the side of the original triangle is: 2 × 3 = 6cm.
(According to the figure, the side of the original triangle is 3 times of a small
triangle.)
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