{"id":599,"date":"2019-01-31T08:41:58","date_gmt":"2019-01-31T13:41:58","guid":{"rendered":"http:\/\/josmfs.net\/?p=599"},"modified":"2024-04-14T20:05:42","modified_gmt":"2024-04-15T00:05:42","slug":"right-triangle-with-roots","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2019\/01\/31\/right-triangle-with-roots\/","title":{"rendered":"Right Triangle with Roots"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-3909\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Right-Triangle-w-roots-Fig2.jpg\" alt=\"\" width=\"201\" height=\"156\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Right-Triangle-w-roots-Fig2.jpg 403w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Right-Triangle-w-roots-Fig2-300x233.jpg 300w\" sizes=\"auto, (max-width: 201px) 100vw, 201px\" \/>This is an interesting problem from the United Kingdom Mathematics Trust (UKMT) Senior Math Challenge of 2008.<\/p>\n<p>\u201cThe length of the hypotenuse of a particular right-angled triangle is given by \u221a(1 + 3 + 5 + \u2026 + 23 + 25). The lengths of the other two sides are given by \u221a(1 + 3 + 5 + \u2026 + (x \u2013 2) + x) and \u221a (1 + 3 + 5 + \u2026 + (y \u2013 2) + y) where x and y are positive integers. What is the value of x + y?\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Right-Triangle-w-Roots-Answer.jpg\">Answer.<\/a><\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/01\/Right-Triangle-with-Roots-190129.pdf\">Right Triangle with Roots<\/a> for a solution.<\/p>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is an interesting problem from the United Kingdom Mathematics Trust (UKMT) Senior Math Challenge of 2008. \u201cThe length of the hypotenuse of a particular right-angled triangle is given by \u221a(1 + 3 + 5 + \u2026 + 23 + 25). The lengths of the other two sides are given by \u221a(1 + 3 + [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[30,83],"class_list":["post-599","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-pythagorean-theorem","tag-ukmt-challenge"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/599","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=599"}],"version-history":[{"count":4,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/599\/revisions"}],"predecessor-version":[{"id":3911,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/599\/revisions\/3911"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=599"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=599"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=599"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}