{"id":24852,"date":"2023-04-04T23:34:07","date_gmt":"2023-04-04T22:34:07","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24852"},"modified":"2023-04-04T23:49:11","modified_gmt":"2023-04-04T22:49:11","slug":"um-quadrado-e-um-retangulo-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24852","title":{"rendered":"Um quadrado e um ret\u00e2ngulo"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24852' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24852' class='GTTabs_curr'><a  id=\"24852_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24852' ><a  id=\"24852_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_24852'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Se aumentarmos 1 cm e 3 cm a dois lados adjacentes de um quadrado, obtemos um ret\u00e2ngulo cuja \u00e1rea excede em 5 cm<sup>2<\/sup> a \u00e1rea do quadrado inicial.<\/p>\n<p>Quais s\u00e3o as dimens\u00f5es do ret\u00e2ngulo?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24852' onClick='GTTabs_show(1,24852)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24852'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Se aumentarmos 1 cm e 3 cm a dois lados adjacentes de um quadrado, obtemos um ret\u00e2ngulo cuja \u00e1rea excede em 5 cm<sup>2<\/sup> a \u00e1rea do quadrado inicial.<\/p>\n<p>Quais s\u00e3o as dimens\u00f5es do ret\u00e2ngulo?<\/p>\n<\/blockquote>\n<p>\u00a0<\/p>\n<p>Designemos por \\(x\\) o comprimento, em cent\u00edmetros, do lado do quadrado.<br \/>Assim, e em cm<sup>2<\/sup>, as \u00e1reas do quadrado e do ret\u00e2ngulo ser\u00e3o expressas, respetivamente, por:<\/p>\n<ul>\n<li>\\({x^2}\\)<\/li>\n<li>\\(\\left( {x + 1} \\right)\\left( {x + 3} \\right)\\)<\/li>\n<\/ul>\n<p>Equacionando o problema e resolvendo a equa\u00e7\u00e3o, vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\left( {x + 1} \\right)\\left( {x + 3} \\right) &#8211; {x^2} = 5}&amp; \\Leftrightarrow &amp;{{x^2} + 3x + x + 3 &#8211; {x^2} = 5}\\\\{}&amp; \\Leftrightarrow &amp;{4x = 2}\\\\{}&amp; \\Leftrightarrow &amp;{x = \\frac{1}{2}}\\end{array}\\]<\/p>\n<p>Portanto, o ret\u00e2ngulo tem as seguintes dimens\u00f5es: \\({1,5^{cm}} \\times {3,5^{cm}}\\).<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24852' onClick='GTTabs_show(0,24852)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Se aumentarmos 1 cm e 3 cm a dois lados adjacentes de um quadrado, obtemos um ret\u00e2ngulo cuja \u00e1rea excede em 5 cm2 a \u00e1rea do quadrado inicial. Quais s\u00e3o as&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19177,"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],"series":[],"class_list":["post-24852","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"],"views":77,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat68.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24852","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=24852"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24852\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19177"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24852"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24852"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24852"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24852"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}