{"id":24951,"date":"2023-04-10T16:20:28","date_gmt":"2023-04-10T15:20:28","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24951"},"modified":"2023-04-10T16:35:26","modified_gmt":"2023-04-10T15:35:26","slug":"um-quadrado-e-um-retangulo-com-igual-area","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24951","title":{"rendered":"Um quadrado e um ret\u00e2ngulo com igual \u00e1rea"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24951' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24951' class='GTTabs_curr'><a  id=\"24951_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24951' ><a  id=\"24951_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_24951'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>A professora de Matem\u00e1tica do C\u00e9sar disse-lhe que o quadrado e o ret\u00e2ngulo da figura t\u00eam a mesma medida de \u00e1rea.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag153-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"24952\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=24952\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag153-6.png\" data-orig-size=\"470,161\" 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_Pag153-6\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag153-6.png\" class=\"aligncenter wp-image-24952\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag153-6-300x103.png\" alt=\"\" width=\"400\" height=\"137\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag153-6-300x103.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag153-6.png 470w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a><\/p>\n<p>Qual \u00e9 o valor de <em>x<\/em>?<br \/>Apresenta todos os c\u00e1lculos efetuados.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24951' onClick='GTTabs_show(1,24951)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24951'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>A professora de Matem\u00e1tica do C\u00e9sar disse-lhe que o quadrado e o ret\u00e2ngulo da figura t\u00eam a mesma medida de \u00e1rea.<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag153-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"24952\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=24952\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag153-6.png\" data-orig-size=\"470,161\" 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_Pag153-6\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag153-6.png\" class=\"aligncenter wp-image-24952\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag153-6-300x103.png\" alt=\"\" width=\"400\" height=\"137\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag153-6-300x103.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag153-6.png 470w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a><\/p>\n<blockquote>\n<p>Qual \u00e9 o valor de <em>x<\/em>?<br \/>Apresenta todos os c\u00e1lculos efetuados.<\/p>\n<\/blockquote>\n<p>\u00a0<\/p>\n<p>Apreciando as medidas expressas nos lados dos quadril\u00e1teros, podemos concluir que ter\u00e1 de ser \\(x &gt; 4\\). Equacionando o problema e resolvendo a equa\u00e7\u00e3o, vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{{\\left( {x + 2} \\right)}^2} = \\left( {2x &#8211; 1} \\right)\\left( {x &#8211; 4} \\right)}&amp; \\Leftrightarrow &amp;{{x^2} + 4x + 4 = 2{x^2} &#8211; 8x &#8211; x + 4}\\\\{}&amp; \\Leftrightarrow &amp;{{x^2} + 4x + 4 &#8211; 2{x^2} + 8x + x &#8211; 4 = 0}\\\\{}&amp; \\Leftrightarrow &amp;{ &#8211; {x^2} + 13x = 0}\\\\{}&amp; \\Leftrightarrow &amp;{ &#8211; x\\left( {x &#8211; 13} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{ &#8211; x = 0}&amp; \\vee &amp;{x &#8211; 13 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 0}&amp; \\vee &amp;{x = 13}\\end{array}}\\end{array}\\]<\/p>\n<p>Ainda que a equa\u00e7\u00e3o admita duas solu\u00e7\u00f5es, o problema apenas admite a solu\u00e7\u00e3o \\(x = 13\\).<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24951' onClick='GTTabs_show(0,24951)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A professora de Matem\u00e1tica do C\u00e9sar disse-lhe que o quadrado e o ret\u00e2ngulo da figura t\u00eam a mesma medida de \u00e1rea. Qual \u00e9 o valor de x?Apresenta todos os c\u00e1lculos efetuados.&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":24953,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,700],"tags":[424,196,706,198,195],"series":[],"class_list":["post-24951","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-casos-notaveis","tag-equacao-incompleta-do-2-o-grau","tag-lei-do-anulamento-do-produto","tag-operacoes-com-polinomios"],"views":141,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag153-6_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24951","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=24951"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24951\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/24953"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24951"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24951"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24951"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24951"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}