{"id":24544,"date":"2023-03-07T21:59:34","date_gmt":"2023-03-07T21:59:34","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24544"},"modified":"2023-03-07T22:43:53","modified_gmt":"2023-03-07T22:43:53","slug":"um-quadrado-dividido-em-quatro-quadrilateros","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24544","title":{"rendered":"Um quadrado dividido em cinco quadril\u00e1teros"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24544' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24544' class='GTTabs_curr'><a  id=\"24544_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24544' ><a  id=\"24544_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_24544'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Na seguinte figura, um quadrado de lado x + y foi dividido em quatro ret\u00e2ngulos iguais e um quadrado.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag136-7.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"24545\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=24545\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag136-7.png\" data-orig-size=\"393,396\" 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=\"8Pag136-7\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag136-7.png\" class=\"aligncenter wp-image-24545\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag136-7-298x300.png\" alt=\"\" width=\"240\" height=\"242\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag136-7-298x300.png 298w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag136-7-150x150.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag136-7-80x80.png 80w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag136-7.png 393w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a><\/p>\n<ol>\n<li>Justifica que o quadril\u00e1tero central \u00e9 um quadrado e indica uma express\u00e3o para o lado desse quadrado como um polin\u00f3mio de vari\u00e1veis x e y.<\/li>\n<li>Exprime a \u00e1rea dos ret\u00e2ngulos e do quadrado central atrav\u00e9s de polin\u00f3mios nas vari\u00e1veis x e y.<\/li>\n<li>Utilizando a al\u00ednea anterior, mostra que \\({\\left( {x + y} \\right)^2} = 4xy + {\\left( {x &#8211; y} \\right)^2}\\).<\/li>\n<li>Prova algebricamente a igualdade da al\u00ednea anterior.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24544' onClick='GTTabs_show(1,24544)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24544'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Na seguinte figura, um quadrado de lado x + y foi dividido em quatro ret\u00e2ngulos iguais e um quadrado.<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag136-7.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"24545\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=24545\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag136-7.png\" data-orig-size=\"393,396\" 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=\"8Pag136-7\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag136-7.png\" class=\"aligncenter wp-image-24545\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag136-7-298x300.png\" alt=\"\" width=\"240\" height=\"242\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag136-7-298x300.png 298w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag136-7-150x150.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag136-7-80x80.png 80w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag136-7.png 393w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a><\/p>\n<ol>\n<li>\n<blockquote>Justifica que o quadril\u00e1tero central \u00e9 um quadrado e indica uma express\u00e3o para o lado desse quadrado como um polin\u00f3mio de vari\u00e1veis x e y.<\/blockquote>\n<\/li>\n<li>\n<blockquote>Exprime a \u00e1rea dos ret\u00e2ngulos e do quadrado central atrav\u00e9s de polin\u00f3mios nas vari\u00e1veis x e y.<\/blockquote>\n<\/li>\n<li>\n<blockquote>Utilizando a al\u00ednea anterior, mostra que \\({\\left( {x + y} \\right)^2} = 4xy + {\\left( {x &#8211; y} \\right)^2}\\).<\/blockquote>\n<\/li>\n<li>\n<blockquote>Prova algebricamente a igualdade da al\u00ednea anterior.<\/blockquote>\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ol>\n<li>O quadril\u00e1tero central \u00e9 um quadrado, pois os seus \u00e2ngulos internos s\u00e3o retos e os seus lados s\u00e3o iguais.<br \/>Uma express\u00e3o para o lado do quadrado pode ser: \\(l = \\left( {x + y} \\right) &#8211; 2y = x &#8211; y\\).<br \/><br \/><\/li>\n<li>A \u00e1rea dos ret\u00e2ngulos pode ser expressa por: \\({A_{{\\rm{Ret\u00e2ngulos}}}} = 4 \\times \\left( {xy} \\right) = 4xy\\).<br \/>A \u00e1rea do quadrado pode ser expressa por: \\({A_{{\\rm{Quadrado}}}} = {\\left( {x &#8211; y} \\right)^2}\\).<br \/><br \/><\/li>\n<li>A \u00e1rea do quadrado de lado x + y foi decomposto em quatro ret\u00e2ngulos iguais e um quadrado central.<br \/>Assim, temos: \\(\\begin{array}{*{20}{c}}{{A_{QI}} = {A_{{\\rm{Ret\u00e2ngulos}}}} + {A_{{\\rm{Quadrado}}}}}&amp; \\Leftrightarrow &amp;{{{\\left( {x + y} \\right)}^2} = 4xy + {{\\left( {x &#8211; y} \\right)}^2}}\\end{array}\\).<br \/><br \/><\/li>\n<li><br \/>\\[\\begin{array}{*{20}{l}}{4xy + {{\\left( {x &#8211; y} \\right)}^2}}&amp; = &amp;{4xy + {x^2} &#8211; 2xy + {y^2}}\\\\{}&amp; = &amp;{{x^2} + 2xy + {y^2}}\\\\{}&amp; = &amp;{{{\\left( {x + y} \\right)}^2}}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24544' onClick='GTTabs_show(0,24544)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na seguinte figura, um quadrado de lado x + y foi dividido em quatro ret\u00e2ngulos iguais e um quadrado. Justifica que o quadril\u00e1tero central \u00e9 um quadrado e indica uma express\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":24546,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,700],"tags":[424,196,194],"series":[],"class_list":["post-24544","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-monomios"],"views":137,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag136-7_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24544","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=24544"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24544\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/24546"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24544"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24544"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24544"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24544"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}