Grades 3-4 Video Solutions 2020-2020Levels34prob16

2020Levels34prob16

Video Transcription

Problem number 16. Farid has two types of sticks. Short ones measuring one centimeter and long ones measuring three centimeters. With which of the  combinations below can he make a square without breaking or overlapping the sticks? A. Five short and two long. B. Three short and three long. C. Six short. D. Four  short and two long. E. Six long. We know that a square has four equal sides. So we need to figure out which of these combinations of sticks can be used to  make four sides of the same length. We also know that a short stick is one centimeter long and a long stick is three centimeters long. This means that  three short sticks are equal to one long stick. The problem tells us that Farid cannot break any of the sticks. So in any of the answers where only one type of  stick is mentioned, that would be in C and in E, the number of sticks would need to be divisible by four. However, each one of these lists six sticks and six is not  divisible by four. You cannot make a square out of six sticks without breaking them. So C and E cannot be the right answers. Since we know that three short sticks are the same as  one long stick, answer B looks promising. And in fact, if we write down one long instead of three short here, we come out with saying that this is the same as  four long sticks. And obviously, we use four long sticks, we can make a square. So B should be the correct answer. Let's just look at the other remaining answers.  If we have five short sticks and two long sticks, as in answer A, we start building a square with a long stick here, a long stick here. We can make one  side out of three of the short sticks. And we start building the second side. And we do not have enough sticks to complete the square. In answer D, we have  four short sticks and two long sticks. So this will be very similar. We can make one side of a long stick here, another side of a long stick, a side using three short  sticks, and we start the fourth side. We cannot complete it. So the only answer that works is B. Farid can use three short and three long sticks to build a square.

Video Summary

Farid wants to create a square using sticks of lengths one centimeter (short) and three centimeters (long). To form a square, four equal-length sides are needed. Analyzing the options, configurations solely with one type of stick, if those sticks aren’t divisible by four, can't form a square. Only option B, using three short and three long sticks, converts effectively into four sides of equal length (equivalent to four long sticks). By rearranging these without breaking any, a square can be made. Therefore, option B is the correct solution to form a square without breaking or overlapping sticks.