Grades 9-10 Video Solutions 2023-2023_9-10

Video Transcription

The diagram shows a map of a park. The park is divided into regions. The number inside each region gives its perimeter in kilometers. What is the outer perimeter of the park?  Let's draw the map with some markings instead of the same numbers that we are using.  We seek the perimeter of the park, which is just this outermost border.  Then, to find the outermost border, we can find A plus B plus C plus D plus E as the perimeter.  However, note that that also included this dashed line right here as part of our sum.  We want to get rid of this, so we do A plus C plus D plus E minus F, G, and H in order to get rid of the dashed lines that we just talked about.  However, when we get rid of those dashed lines, that also gets rid of the dotted lines because we subtracted G, F, and H.  Because we subtracted the dotted line and we don't want to subtract the dotted line, we need to re-add K.  We add back K, and therefore the total length of the perimeter is A plus B plus C plus D plus E minus F, G, and H.  Then, we add K back on to get 42 minus 20 plus 4, which we find to be 26 kilometers, which is our answer.

Video Summary

The problem involves finding the perimeter of a park by analyzing its divided regions on a map. The initial calculation includes the outer and some inner lines as parts of the perimeter. To correct this, the inner dashed lines (F, G, and H) are subtracted from the initial sum, as these were mistakenly included. However, this subtraction also inadvertently removes the necessary dotted line (K), which needs to be re-added to accurately reflect the outer perimeter. The final calculation is \(42 - 20 + 4\), resulting in a total perimeter of 26 kilometers.

Keywords

perimeter calculation

park map analysis

inner dashed lines

outer perimeter

corrected perimeter