{"id":14384,"date":"2018-04-11T10:17:32","date_gmt":"2018-04-11T09:17:32","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14384"},"modified":"2022-01-06T22:54:57","modified_gmt":"2022-01-06T22:54:57","slug":"areas-e-perimetros-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14384","title":{"rendered":"\u00c1reas e per\u00edmetros 2"},"content":{"rendered":"<p><ul id='GTTabs_ul_14384' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14384' class='GTTabs_curr'><a  id=\"14384_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14384' ><a  id=\"14384_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_14384'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14385\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14385\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-2.png\" data-orig-size=\"333,345\" 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=\"Quadrados\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-2.png\" class=\"alignright wp-image-14385\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-2-290x300.png\" alt=\"\" width=\"220\" height=\"228\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-2-290x300.png 290w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-2.png 333w\" sizes=\"auto, (max-width: 220px) 100vw, 220px\" \/><\/a>Na figura, sabe-se que:<\/p>\n<ul>\n<li>[ACEF] \u00e9 um quadrado;<\/li>\n<li>[BCDG] \u00e9 um quadrado;<\/li>\n<li>\\(\\overline {AC} = x\\) cm;<\/li>\n<li>\\(\\overline {BC} = 8\\) cm.<\/li>\n<\/ul>\n<ol>\n<li>Escreve uma express\u00e3o simplificada para o per\u00edmetro da regi\u00e3o sombreada.<br \/>\nMostra como chegaste \u00e0 tua resposta.<\/li>\n<li>Mostra que se\u00a0\\(x = 9\\) cm, ent\u00e3o a \u00e1rea da parte sombreada \u00e9 igual a 17 cm<sup>2<\/sup>.<\/li>\n<li>Escreve uma express\u00e3o simplificada para a \u00e1rea da regi\u00e3o sombreada, na vari\u00e1vel x.<\/li>\n<li>Determina o valor de x para qual a \u00e1rea sombreada \u00e9 igual a 80 cm<sup>2<\/sup>.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14384' onClick='GTTabs_show(1,14384)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14384'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ul>\n<li>\n<blockquote><p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14385\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14385\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-2.png\" data-orig-size=\"333,345\" 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=\"Quadrados\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-2.png\" class=\"alignright wp-image-14385\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-2-290x300.png\" alt=\"\" width=\"220\" height=\"228\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-2-290x300.png 290w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-2.png 333w\" sizes=\"auto, (max-width: 220px) 100vw, 220px\" \/><\/a>[ACEF] \u00e9 um quadrado;<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>[BCDG] \u00e9 um quadrado;<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>\\(\\overline {AC} = x\\) cm;<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>\\(\\overline {BC} = 8\\) cm.<\/p><\/blockquote>\n<\/li>\n<\/ul>\n<p>\u00ad<\/p>\n<ol>\n<li>Apresenta-se seguidamente uma express\u00e3o para o per\u00edmetro da regi\u00e3o sombreada:<br \/>\n\\[\\begin{array}{*{20}{l}}{P\\left( x \\right)}&amp; = &amp;{\\overline {AB} + \\overline {BG} + \\overline {GD} + \\overline {DE} + \\overline {EF} + \\overline {FA} }\\\\{}&amp; = &amp;{\\left( {x &#8211; 8} \\right) + 8 + 8 + \\left( {x &#8211; 8} \\right) + x + x}\\\\{}&amp; = &amp;{4x}\\end{array}\\]<\/li>\n<li>Se\u00a0\\(x = 9\\) cm, ent\u00e3o a \u00e1rea da parte sombreada \u00e9 igual a 17 cm<sup>2<\/sup>:<br \/>\n\\[A\\left( 9 \\right) = 2 \\times \\frac{{\\overline {AF} + \\overline {BG} }}{2} \\times \\overline {AB} = 2 \\times \\frac{{9 + 8}}{2} \\times 1 = 17\\]<\/li>\n<li>Uma express\u00e3o simplificada para a \u00e1rea da regi\u00e3o sombreada, na vari\u00e1vel x, \u00e9:<br \/>\n\\[\\begin{array}{*{20}{l}}{A\\left( x \\right)}&amp; = &amp;{2 \\times \\frac{{x + 8}}{2} \\times \\left( {x &#8211; 8} \\right)}\\\\{}&amp; = &amp;{\\left( {x + 8} \\right) \\times \\left( {x &#8211; 8} \\right)}\\\\{}&amp; = &amp;{{x^2} &#8211; 64}\\end{array}\\]<\/li>\n<li>A \u00e1rea sombreada \u00e9 igual a 80 cm<sup>2<\/sup> para\u00a0\\(x = 12\\):<br \/>\n\\[\\begin{array}{*{20}{l}}{A\\left( x \\right) = 80}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{{x^2} &#8211; 64 = 80}&amp; \\wedge &amp;{x &gt; 8}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{{x^2} = 144}&amp; \\wedge &amp;{x &gt; 8}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{\\left( {\\begin{array}{*{20}{c}}{x = &#8211; 12}&amp; \\vee &amp;{x = 12}\\end{array}} \\right)}&amp; \\wedge &amp;{x &gt; 8}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{x = 12}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14384' onClick='GTTabs_show(0,14384)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura, sabe-se que: [ACEF] \u00e9 um quadrado; [BCDG] \u00e9 um quadrado; \\(\\overline {AC} = x\\) cm; \\(\\overline {BC} = 8\\) cm. Escreve uma express\u00e3o simplificada para o per\u00edmetro da regi\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14386,"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],"series":[],"class_list":["post-14384","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"],"views":3731,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag78-1-2a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14384","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=14384"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14384\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14386"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14384"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14384"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14384"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14384"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}