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Question

Hi, need help to understand why the answer is not 21.5cm for this question. 

Matthew had 1.5 m of copper wire. He used it to bend into the shape shown in the figure below. In the figure, there are 6 equilateral triangles. He had 21 cm of the copper wire left. What was the length of AB?

thank you.

Answer

The amount of wire used to bend into the shape is 1.5 m – 0.21 m = 1.29 m

If length of AB is u m,

5u = 1.29

u = 0.25

So the length of AB is 0.258 m or 25.8 cm.

Think your answer is considering 6u = 1.29. But actually the horizontal line is shared between two equilateral triangles, so in total there are only 5u. 

 

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thanks for response! 

just wonder why is there a 5u?

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Not sure if this appear more appropriate:

1.5m = 150cm

150-21=129cm

Since they are formed by equilateral triangles, we assume all lines that formed them are equal; therefore, we consider them as 15 lines = 15u

15u=129

u=129/15=8.6cm

Since length of AB formed by 3 lines or 3u,

3u=8.6 x 3 = 25.8cm.

please advise. Thanks. 

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Think 15u not appropriate, as u is length of AB and formed by sum of length of 3 different sized equilateral triangles with different lengths ( by looking at the horizontal line). So u is the sum of these 3 different lengths and there are 5 sets of these lines formed by the wire.

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There are 6 equilateral triangles ( 1 triangle 3 length, 2 triangles 6 length), so if length AB are splitted into 3 different length each represented by the length of different sized equilateral triangle, the wire length should be 6( length of small triangle + medium triangle + large triangle) = 6u. However, since the horizontal line are shared by 2 triangles, so there are actually 5u. 

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