{"id":26208,"date":"2023-06-05T00:08:31","date_gmt":"2023-06-04T23:08:31","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=26208"},"modified":"2023-06-05T00:23:25","modified_gmt":"2023-06-04T23:23:25","slug":"um-retangulo-com-28-cm-de-perimetro","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=26208","title":{"rendered":"Um ret\u00e2ngulo com 28 cm de per\u00edmetro"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_26208' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_26208' class='GTTabs_curr'><a  id=\"26208_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_26208' ><a  id=\"26208_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_26208'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Um ret\u00e2ngulo tem 28 cm de per\u00edmetro. O comprimento tem 2 cm a mais que a largura.<br \/>Quais s\u00e3o as dimens\u00f5es desse ret\u00e2ngulo?<\/p>\n<p><strong>[A]<\/strong> 3 cm e 5cm.<br \/><strong>[B]<\/strong> 8 cm e 6 cm.<br \/><strong>[C]<\/strong> 4 cm e 6 cm.<br \/><strong>[D]<\/strong> 8 cm e 10 cm.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_26208' onClick='GTTabs_show(1,26208)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_26208'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Um ret\u00e2ngulo tem 28 cm de per\u00edmetro. O comprimento tem 2 cm a mais que a largura.<br \/>Quais s\u00e3o as dimens\u00f5es desse ret\u00e2ngulo?<\/p>\n<p><strong>[A]<\/strong> 3 cm e 5cm.<br \/><strong>[B]<\/strong> 8 cm e 6 cm.<br \/><strong>[C]<\/strong> 4 cm e 6 cm.<br \/><strong>[D]<\/strong> 8 cm e 10 cm.<\/p>\n<\/blockquote>\n<p><br \/>Se o ret\u00e2ngulo tem 28 cm de per\u00edmetro, ent\u00e3o o seu semi-per\u00edmetro \u00e9 14 cm.<br \/>Como o comprimento tem 2 cm a mais que a largura, ent\u00e3o as suas dimens\u00f5es apenas podem ser as da op\u00e7\u00e3o <strong>[B]<\/strong>.<\/p>\n<p>\u00a0<\/p>\n<h6>Alternativa envolvendo um sistema de equa\u00e7\u00f5es<\/h6>\n<p>Designemos o comprimento e a largura do ret\u00e2ngulo por <em>x<\/em> e <em>y<\/em>, respetivamente, e em cent\u00edmetros.<\/p>\n<p>Equacionando o problema e resolvendo o sistema de equa\u00e7\u00f5es, vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\left\\{ {\\begin{array}{*{20}{l}}{2x + 2y = 28}\\\\{x = y + 2}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{x = y + 2}\\\\{2y + 4 + 2y = 28}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{4y = 24}\\\\{x = y + 2}\\end{array}} \\right.}&amp; \\Leftrightarrow \\\\{}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{y = 6}\\\\{x = 8}\\end{array}} \\right.}&amp;{}&amp;{}&amp;{}\\end{array}\\]<\/p>\n<p>Portanto, a op\u00e7\u00e3o correta \u00e9 <strong>[B]<\/strong> 8 cm e 6 cm.<\/p>\n<p>\u00a0<\/p>\n<p>\u00a0<\/p>\n<p>\u00a0<\/p>\n<p>\u00a0<\/p>\n\n\n\n<p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_26208' onClick='GTTabs_show(0,26208)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um ret\u00e2ngulo tem 28 cm de per\u00edmetro. O comprimento tem 2 cm a mais que a largura.Quais s\u00e3o as dimens\u00f5es desse ret\u00e2ngulo? [A] 3 cm e 5cm.[B] 8 cm e 6&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19171,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,714],"tags":[424,345,239],"series":[],"class_list":["post-26208","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-literais-e-sistemas","tag-8-o-ano","tag-funcao-afim","tag-sistema-de-equacoes"],"views":81,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat62.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26208","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=26208"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26208\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19171"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26208"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26208"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26208"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=26208"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}