{"id":14487,"date":"2018-04-14T13:08:39","date_gmt":"2018-04-14T12:08:39","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14487"},"modified":"2022-01-16T12:24:47","modified_gmt":"2022-01-16T12:24:47","slug":"um-triangulo-retangulo-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14487","title":{"rendered":"Um tri\u00e2ngulo ret\u00e2ngulo"},"content":{"rendered":"<p><ul id='GTTabs_ul_14487' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14487' class='GTTabs_curr'><a  id=\"14487_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14487' ><a  id=\"14487_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_14487'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-14.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14491\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14491\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-14.png\" data-orig-size=\"245,245\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Tri\u00e2ngulo ret\u00e2ngulo\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-14.png\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-14.png\" class=\"alignright wp-image-14491\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-14.png\" alt=\"\" width=\"180\" height=\"180\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-14.png 245w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-14-150x150.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-14-160x160.png 160w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-14-320x320.png 320w\" sizes=\"auto, (max-width: 180px) 100vw, 180px\" \/><\/a>Determina as medidas dos lados de um tri\u00e2ngulo ret\u00e2ngulo, sabendo que essas medidas s\u00e3o dadas por n\u00fameros pares consecutivos.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14487' onClick='GTTabs_show(1,14487)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14487'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-14.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14491\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14491\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-14.png\" data-orig-size=\"245,245\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Tri\u00e2ngulo ret\u00e2ngulo\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-14.png\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-14.png\" class=\"alignright wp-image-14491\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-14.png\" alt=\"\" width=\"180\" height=\"180\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-14.png 245w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-14-150x150.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-14-160x160.png 160w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-14-320x320.png 320w\" sizes=\"auto, (max-width: 180px) 100vw, 180px\" \/><\/a>Determina as medidas dos lados de um tri\u00e2ngulo ret\u00e2ngulo, sabendo que essas medidas s\u00e3o dadas por n\u00fameros pares consecutivos.<\/p>\n<\/blockquote>\n<p>\u00ad<\/p>\n<p>Seja \\(n \\in \\mathbb{N}\\).<\/p>\n<p>Assim, as medidas dos lados desse tri\u00e2ngulo ret\u00e2ngulo podem ser expressas por:<\/p>\n<table class=\" aligncenter\" style=\"width: 60%;\">\n<tbody>\n<tr>\n<td>Cateto menor<\/td>\n<td>Cateto maior<\/td>\n<td>Hipotenusa<\/td>\n<\/tr>\n<tr>\n<td>\\(2n\\)<\/td>\n<td>\\(2n + 2\\)<\/td>\n<td>\\(2n + 4\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Assim, por aplica\u00e7\u00e3o do Teorema de Pit\u00e1goras, vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{{\\left( {2n} \\right)}^2} + {{\\left( {2n + 2} \\right)}^2} = {{\\left( {2n + 4} \\right)}^2}}&amp; \\Leftrightarrow &amp;{4{n^2} + 4{n^2} + 8n + 4 = 4{n^2} + 16n + 16}\\\\{}&amp; \\Leftrightarrow &amp;{4{n^2} &#8211; 8n &#8211; 12 = 0}\\\\{}&amp; \\Leftrightarrow &amp;{{n^2} &#8211; 2n &#8211; 3 = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{n = \\frac{{2 + \\sqrt {4 + 12} }}{2}}&amp;{}&amp;{(Ver\\;nota)}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{n = \\frac{{2 + 4}}{2}}\\\\{}&amp; \\Leftrightarrow &amp;{n = 3}\\end{array}\\]<\/p>\n<p><strong>Nota<\/strong>: Como\u00a0\\(n \\in \\mathbb{N}\\), um n\u00famero negativo n\u00e3o pode ser solu\u00e7\u00e3o da equa\u00e7\u00e3o.<\/p>\n<p>Assim, as medidas dos lados do tri\u00e2ngulo s\u00e3o: 6, 8 e 10.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14487' onClick='GTTabs_show(0,14487)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Determina as medidas dos lados de um tri\u00e2ngulo ret\u00e2ngulo, sabendo que essas medidas s\u00e3o dadas por n\u00fameros pares consecutivos. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20362,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,303],"tags":[426,306,118],"series":[],"class_list":["post-14487","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-equacoes-do-2-o-grau","tag-9-o-ano","tag-equacao-do-2-o-grau","tag-teorema-de-pitagoras"],"views":1818,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag089-14_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14487","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=14487"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14487\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20362"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14487"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14487"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14487"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14487"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}