{"id":14566,"date":"2018-04-15T21:38:08","date_gmt":"2018-04-15T20:38:08","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14566"},"modified":"2026-04-24T17:50:07","modified_gmt":"2026-04-24T16:50:07","slug":"o-pai-do-joao-comprou-um-terreno","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14566","title":{"rendered":"O pai do Jo\u00e3o comprou um terreno"},"content":{"rendered":"<p><ul id='GTTabs_ul_14566' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14566' class='GTTabs_curr'><a  id=\"14566_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14566' ><a  id=\"14566_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_14566'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-8.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14567\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14567\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-8.png\" data-orig-size=\"432,400\" 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=\"Terreno\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-8.png\" class=\"alignright size-medium wp-image-14567\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-8-300x278.png\" alt=\"\" width=\"300\" height=\"278\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-8-300x278.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-8.png 432w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>O pai do Jo\u00e3o comprou um terreno com a forma de um quadrado.<br \/>\nNuma parte retangular desse terreno, o Jo\u00e3o vai fazer um jardim com 28 m<sup>2<\/sup> de \u00e1rea, como mostra a figura.<\/p>\n<p>Qual \u00e9 a medida do lado do terreno?<br \/>\nExplica a tua resposta.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14566' onClick='GTTabs_show(1,14566)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14566'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-8.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14567\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14567\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-8.png\" data-orig-size=\"432,400\" 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=\"Terreno\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-8.png\" class=\"alignright size-medium wp-image-14567\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-8-300x278.png\" alt=\"\" width=\"300\" height=\"278\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-8-300x278.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-8.png 432w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Seja <em>x<\/em>, em metros, o comprimento do lado do terreno com a forma quadrada.<\/p>\n<p>A \u00e1rea do jardim pode ser expressa, em fun\u00e7\u00e3o de <em>x<\/em>, por:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{A_{Jardim }}}&amp; = &amp;{\\left( {x &#8211; 8} \\right)\\left( {x &#8211; 5} \\right)}\\\\{}&amp; = &amp;{{x^2} &#8211; 5x &#8211; 8x + 40}\\\\{}&amp; = &amp;{{x^2} &#8211; 13x + 40}\\end{array}\\]<\/p>\n<p>com\u00a0\\(x &gt; 8\\).<\/p>\n<p>Como o jardim ter\u00e1 28 m<sup>2<\/sup> de \u00e1rea, vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{A_{Jardim }} = 28}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{{x^2} &#8211; 13x + 40 = 28}&amp; \\wedge &amp;{x &gt; 8}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{{x^2} &#8211; 13x + 12 = 0}&amp; \\wedge &amp;{x &gt; 8}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = \\frac{{13 \\mp \\sqrt {169 &#8211; 48} }}{2}}&amp; \\wedge &amp;{x &gt; 2}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{\\left( {\\begin{array}{*{20}{c}}{x = \\frac{{13 &#8211; 11}}{2}}&amp; \\vee &amp;{x = \\frac{{13 + 11}}{2}}\\end{array}} \\right)}&amp; \\wedge &amp;{x &gt; 2}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{x = 12}\\end{array}\\]<\/p>\n<p>Portanto, o terreno tem 8 m de lado.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14566' onClick='GTTabs_show(0,14566)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O pai do Jo\u00e3o comprou um terreno com a forma de um quadrado. Numa parte retangular desse terreno, o Jo\u00e3o vai fazer um jardim com 28 m2 de \u00e1rea, como mostra&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20363,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,303],"tags":[426,108,306,304],"series":[],"class_list":["post-14566","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-equacoes-do-2-o-grau","tag-9-o-ano","tag-area","tag-equacao-do-2-o-grau","tag-formula-resolvente"],"views":2796,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag095-8_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14566","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=14566"}],"version-history":[{"count":1,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14566\/revisions"}],"predecessor-version":[{"id":27682,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14566\/revisions\/27682"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20363"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14566"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14566"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14566"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14566"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}