{"id":24662,"date":"2023-04-01T17:21:56","date_gmt":"2023-04-01T16:21:56","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24662"},"modified":"2023-04-01T17:49:21","modified_gmt":"2023-04-01T16:49:21","slug":"qual-e-o-comprimento-do-retangulo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24662","title":{"rendered":"Qual \u00e9 o comprimento do ret\u00e2ngulo?"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24662' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24662' class='GTTabs_curr'><a  id=\"24662_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24662' ><a  id=\"24662_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_24662'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Num ret\u00e2ngulo, a base mede o dobro da altura.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag145-9.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"24663\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=24663\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag145-9.png\" data-orig-size=\"288,165\" 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_Pag145-9\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag145-9.png\" class=\"wp-image-24663 aligncenter\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag145-9.png\" alt=\"\" width=\"280\" height=\"160\" \/><\/a><\/p>\n<p>Numericamente, verifica-se que adicionando 18 unidades \u00e0 medida da \u00e1rea desse ret\u00e2ngulo se obt\u00e9m o dobro da medida do seu per\u00edmetro.<br \/>Qual \u00e9 o comprimento do ret\u00e2ngulo?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24662' onClick='GTTabs_show(1,24662)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24662'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Num ret\u00e2ngulo, a base mede o dobro da altura.<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag145-9.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"24663\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=24663\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag145-9.png\" data-orig-size=\"288,165\" 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_Pag145-9\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag145-9.png\" class=\"wp-image-24663 aligncenter\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag145-9.png\" alt=\"\" width=\"280\" height=\"160\" \/><\/a><\/p>\n<blockquote>\n<p>Numericamente, verifica-se que adicionando 18 unidades \u00e0 medida da \u00e1rea desse ret\u00e2ngulo se obt\u00e9m o dobro da medida do seu per\u00edmetro.<br \/>Qual \u00e9 o comprimento do ret\u00e2ngulo?<\/p>\n<\/blockquote>\n<p>\u00a0<\/p>\n<p>Equacionando o problema e resolvendo a equa\u00e7\u00e3o, vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{x \\times \\frac{x}{2} + 18 = 2 \\times \\left( {2\\left( {x + \\frac{x}{2}} \\right)} \\right)}&amp; \\Leftrightarrow &amp;{\\frac{{{x^2}}}{2} + 18 = 4x + 2x}\\\\{}&amp; \\Leftrightarrow &amp;{{x^2} + 36 = 12x}\\\\{}&amp; \\Leftrightarrow &amp;{{x^2} &#8211; 12x + 36 = 0}\\\\{}&amp; \\Leftrightarrow &amp;{{{\\left( {x &#8211; 6} \\right)}^2} = 0}\\\\{}&amp; \\Leftrightarrow &amp;{x &#8211; 6 = 0}\\\\{}&amp; \\Leftrightarrow &amp;{x = 6}\\end{array}\\]<\/p>\n<p>Portanto, o ret\u00e2ngulo tem 6 unidades de comprimento.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24662' onClick='GTTabs_show(0,24662)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Num ret\u00e2ngulo, a base mede o dobro da altura. Numericamente, verifica-se que adicionando 18 unidades \u00e0 medida da \u00e1rea desse ret\u00e2ngulo se obt\u00e9m o dobro da medida do seu per\u00edmetro.Qual \u00e9&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":24664,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,700],"tags":[424,706,198,705],"series":[],"class_list":["post-24662","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-monomios-e-polinomios","tag-8-o-ano","tag-equacao-incompleta-do-2-o-grau","tag-lei-do-anulamento-do-produto","tag-polinomios"],"views":78,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag145-9_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24662","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=24662"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24662\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/24664"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24662"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24662"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24662"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24662"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}