# 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.

1 Answer

# 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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