Grades 3-4 Video Solutions 2020-2020Levels34prob12

Video Transcription

Problem number 12. Lanaca builds a fence using 1 meter long poles. The picture shows a 4 meter long fence. How many poles does Lanaca need to build a 10  meter long fence? A, 22. B, 30. C, 33. D, 40. E, 42. In a problem like this, there should be a pattern of how the image that you're making is constructed so that you can  think through what it would look like if it's longer. Here's the pattern. The fence is 4 meters long and each of the horizontal 1 meter pieces gives it its  length. So here are four of them. There is another set which makes a total of 8 horizontal pieces in a 4 meter long fence. Then you have the vertical pieces.  You have one to start out with and one copying it above. And then for each of the horizontal pieces, you get another vertical piece.  So for a four meter long fence,  there are eight horizontal pieces  and 10 vertical pieces,  which correspond to the eight vertical pieces, one for each horizontal and two extras.  So for each meter of length,  there will be two horizontal pieces  and two vertical pieces,  plus there will be two vertical pieces. This means that if the fence is 10 meters long,  there will be 20 horizontal pieces,  20 vertical pieces,  and two more pieces, which are vertical, which gives us a total of 42 pieces.  We can check our answer.  Draw one, two, three, four, five, six, seven, eight, nine, 10 poles to give us our length.  10 more horizontal poles. One, two, three, four, five, six, seven, eight, nine, 10.  The two poles at the front. One, two, three, four, five, six, seven, eight, nine, 10.  10 vertical poles here and 10 more vertical poles here.  So our answer is E, 42.

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