{"id":7317,"date":"2012-01-10T21:19:54","date_gmt":"2012-01-10T21:19:54","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7317"},"modified":"2022-01-08T17:31:55","modified_gmt":"2022-01-08T17:31:55","slug":"um-retangulo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7317","title":{"rendered":"Um ret\u00e2ngulo"},"content":{"rendered":"<p><ul id='GTTabs_ul_7317' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7317' class='GTTabs_curr'><a  id=\"7317_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7317' ><a  id=\"7317_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_7317'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Um ret\u00e2ngulo tem de comprimento $2\\sqrt{3}+2$ e de largura $\\sqrt{3}-1$.<\/p>\n<ol>\n<li>Calcula 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_7317' onClick='GTTabs_show(1,7317)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7317'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Na unidade de comprimento considerada, o per\u00edmetro do ret\u00e2ngulo \u00e9:<br \/>\n$$\\begin{array}{*{35}{l}}<br \/>\nP &amp; = &amp; 2\\times (2\\sqrt{3}+2)+2\\times (\\sqrt{3}-1)\u00a0 \\\\<br \/>\n{} &amp; = &amp; 4\\sqrt{3}+4+2\\sqrt{3}-2\u00a0 \\\\<br \/>\n{} &amp; = &amp; 2+6\\sqrt{3}\u00a0 \\\\<br \/>\n\\end{array}$$<\/li>\n<li>Na unidade de \u00e1rea considerada, a \u00e1rea do ret\u00e2ngulo \u00e9:<br \/>\n$$\\begin{array}{*{35}{l}}<br \/>\nA &amp; = &amp; (2\\sqrt{3}+2)\\times (\\sqrt{3}-1)\u00a0 \\\\<br \/>\n{} &amp; = &amp; 2\\times {{\\left( \\sqrt{3} \\right)}^{2}}-2\\sqrt{3}+2\\sqrt{3}-2\u00a0 \\\\<br \/>\n{} &amp; = &amp; 2\\times 3-2\u00a0 \\\\<br \/>\n{} &amp; = &amp; 4\u00a0 \\\\<br \/>\n\\end{array}$$<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7317' onClick='GTTabs_show(0,7317)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um ret\u00e2ngulo tem de comprimento $2\\sqrt{3}+2$ e de largura $\\sqrt{3}-1$. Calcula o per\u00edmetro do ret\u00e2ngulo. Mostra que a \u00e1rea do ret\u00e2ngulo \u00e9 um n\u00famero inteiro. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14083,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,258],"tags":[426,259,266],"series":[],"class_list":["post-7317","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-os-numeros-reais","tag-9-o-ano","tag-numeros-irracionais","tag-numeros-reais"],"views":2327,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat28.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7317","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=7317"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7317\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14083"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7317"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7317"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7317"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7317"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}