{"id":23029,"date":"2022-11-05T12:27:25","date_gmt":"2022-11-05T12:27:25","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=23029"},"modified":"2022-11-08T21:59:17","modified_gmt":"2022-11-08T21:59:17","slug":"um-retangulo-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=23029","title":{"rendered":"Um ret\u00e2ngulo"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_23029' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_23029' class='GTTabs_curr'><a  id=\"23029_0\" onMouseOver=\"GTTabsShowLinks('Ununciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Ununciado<\/a><\/li>\n<li id='GTTabs_li_1_23029' ><a  id=\"23029_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_23029'>\n<span class='GTTabs_titles'><b>Ununciado<\/b><\/span><\/p>\n<p>Um ret\u00e2ngulo tem de comprimento \\(2\\sqrt 3 + 2\\) e de largura \\(\\sqrt 3 &#8211; 1\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23032\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23032\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag041-10.png\" data-orig-size=\"420,140\" 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=\"8_Pag041-10\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag041-10-300x100.png\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag041-10.png\" class=\"size-medium wp-image-23032 aligncenter\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag041-10-300x100.png\" alt=\"\" width=\"300\" height=\"100\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag041-10-300x100.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag041-10.png 420w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Qual \u00e9 a express\u00e3o simplificada que representa o per\u00edmetro do ret\u00e2ngulo?<\/li>\n<li>Mostra que a \u00e1rea do ret\u00e2ngulo \u00e9 um n\u00famero inteiro.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23029' onClick='GTTabs_show(1,23029)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_23029'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><\/p>\n<blockquote>\n<p>Um ret\u00e2ngulo tem de comprimento \\(2\\sqrt 3 + 2\\) e de largura \\(\\sqrt 3 &#8211; 1\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23032\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23032\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag041-10.png\" data-orig-size=\"420,140\" 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=\"8_Pag041-10\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag041-10-300x100.png\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag041-10.png\" class=\"size-medium wp-image-23032 aligncenter\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag041-10-300x100.png\" alt=\"\" width=\"300\" height=\"100\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag041-10-300x100.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag041-10.png 420w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<\/blockquote>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>\n<blockquote>Qual \u00e9 a express\u00e3o simplificada que representa o per\u00edmetro do ret\u00e2ngulo?<\/blockquote>\n<\/li>\n<li>\n<blockquote>Mostra que a \u00e1rea do ret\u00e2ngulo \u00e9 um n\u00famero inteiro.<\/blockquote>\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>O per\u00edmetro do ret\u00e2ngulo pode ser expresso pela express\u00e3o seguinte:<br \/>\\[P = 2 \\times \\left( {\\left( {2\\sqrt 3 + 2} \\right) + \\left( {\\sqrt 3 &#8211; 1} \\right)} \\right) = 2 \\times \\left( {3\\sqrt 3 + 1} \\right) = 6\\sqrt 3 + 2\\]<\/li>\n<li>De facto, a \u00e1rea do ret\u00e2ngulo \u00e9 expressa por um n\u00famero inteiro:<br \/>\\[A = \\left( {2\\sqrt 3 + 2} \\right) \\times \\left( {\\sqrt 3 &#8211; 1} \\right) = 2 \\times {\\left( {\\sqrt 3 } \\right)^2} &#8211; 2\\sqrt 3 + 2\\sqrt 3 &#8211; 2 = 2 \\times 3 &#8211; 2 = 4\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23029' onClick='GTTabs_show(0,23029)'>&lt;&lt; Ununciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Ununciado Resolu\u00e7\u00e3o Ununciado Um ret\u00e2ngulo tem de comprimento \\(2\\sqrt 3 + 2\\) e de largura \\(\\sqrt 3 &#8211; 1\\). Qual \u00e9 a express\u00e3o simplificada que representa o per\u00edmetro do ret\u00e2ngulo? Mostra que a \u00e1rea&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":23033,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,258],"tags":[424,259,450],"series":[],"class_list":["post-23029","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-os-numeros-reais","tag-8-o-ano","tag-numeros-irracionais","tag-operacoes-com-numeros-reais"],"views":466,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag041-10_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23029","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=23029"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23029\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/23033"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23029"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23029"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23029"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=23029"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}