tag:blogger.com,1999:blog-5541500.post3353380600244289831..comments2019-10-22T19:41:45.156+09:00Comments on BigHominid's Hairy Chasms: geometry problem fo' yo' assKevin Kimhttp://www.blogger.com/profile/01328790917314282058noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-5541500.post-73621636632991740062019-02-13T02:43:46.816+09:002019-02-13T02:43:46.816+09:00Fast way, it took me more than one minute, but les...Fast way, it took me more than one minute, but less than 10. And I am almost 63.<br />Label all of the areas NOT in yellow:<br />a = the red area<br />b = the area below that<br />c = the area to the right of the red area<br />d = the area below 79<br />e = the area below 72<br />f = the area to right of 72<br />g = the area below 10<br />(It takes a lot longer to explain it than to label it.)<br />Now, use the triangle formulas A = 1/2(b + h). Also, for a parallelogram, the length of top = length of bottom, and<br />length of right = length of left<br />If you go horizontally across the figure, <br />there are 2 triangles whose bases are part of the top and 2 triangle whose bases are part of the bottom. The heights are the same.<br />So (a + b) + (72 + e + 8) = (c + 79 + d) + (f + 10 + g)<br />if you go vertically, there is one triangle whose base is the left side and two triangle whose base is the right side. Again, the heights are the same.<br />So (a + c + 72 + f) + (d + 8 + g) = (b + 79 + e + 10)<br />And, amazingly, all of the letters cancel out except a, the red area. <br />a = 9<br /><br /><br />Danhttps://www.blogger.com/profile/06786977592066687249noreply@blogger.comtag:blogger.com,1999:blog-5541500.post-38270969645934220232018-04-10T00:20:29.009+09:002018-04-10T00:20:29.009+09:00I was thinking something similar. The only way to...I was thinking something similar. The only way to solve the problem in under a minute is to have (recently) memorized the specific geometric properties relevant to this particular problem. So I suspect that the math students had just done a unit on triangles and parallelograms and had this "quickie" method fresh in their minds.Kevin Kimhttps://www.blogger.com/profile/01328790917314282058noreply@blogger.comtag:blogger.com,1999:blog-5541500.post-33360161041191847732018-04-10T00:02:34.414+09:002018-04-10T00:02:34.414+09:00I've gotten more stupid as I age. I could fol...I've gotten more stupid as I age. I could follow the explanation, but I doubt that the reputed Chinese fifth graders used the method shown. I suspect that if they did it in less than a minute, they didn't go through the formal methods shown.<br /><br />BillAnonymousnoreply@blogger.com