{"id":23681,"date":"2022-12-10T23:49:10","date_gmt":"2022-12-10T23:49:10","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=23681"},"modified":"2022-12-28T00:02:04","modified_gmt":"2022-12-28T00:02:04","slug":"um-retangulo-3","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=23681","title":{"rendered":"Um ret\u00e2ngulo"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_23681' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_23681' class='GTTabs_curr'><a  id=\"23681_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_23681' ><a  id=\"23681_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_23681'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Na figura, est\u00e1 representado um ret\u00e2ngulo [ABCD].<br \/>Os v\u00e9rtices A e D s\u00e3o pontos da reta real.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23682\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23682\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-3.png\" data-orig-size=\"379,157\" 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_Pag070-3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-3.png\" class=\"wp-image-23682 aligncenter\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-3-300x124.png\" alt=\"\" width=\"320\" height=\"133\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-3-300x124.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-3.png 379w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/a><\/p>\n<p>Sabe-se ainda que:<\/p>\n<ul style=\"list-style-type: disc;\">\n<li>o ponto E \u00e9 um ponto da reta real;<\/li>\n<li>\\(\\overline {AB} = 2\\), \\(\\overline {BC} = 4\\) e \\(\\overline {AE} = \\overline {AC} \\);<\/li>\n<li>ao ponto A corresponde o n\u00famero \\(1 &#8211; \\sqrt {20} \\).<\/li>\n<\/ul>\n<p>Determina o n\u00famero que corresponde ao ponto E.<br \/>Mostra como chegaste \u00e0 tua resposta.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23681' onClick='GTTabs_show(1,23681)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_23681'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Na figura, est\u00e1 representado um ret\u00e2ngulo [ABCD].<br \/>Os v\u00e9rtices A e D s\u00e3o pontos da reta real.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23682\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23682\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-3.png\" data-orig-size=\"379,157\" 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_Pag070-3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-3.png\" class=\"wp-image-23682 aligncenter\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-3-300x124.png\" alt=\"\" width=\"320\" height=\"133\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-3-300x124.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-3.png 379w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/a><\/p>\n<p>Sabe-se ainda que:<\/p>\n<\/blockquote>\n<ul style=\"list-style-type: disc;\">\n<li>\n<blockquote>o ponto E \u00e9 um ponto da reta real;<\/blockquote>\n<\/li>\n<li>\n<blockquote>\\(\\overline {AB} = 2\\), \\(\\overline {BC} = 4\\) e \\(\\overline {AE} = \\overline {AC} \\);<\/blockquote>\n<\/li>\n<li>\n<blockquote>ao ponto A corresponde o n\u00famero \\(1 &#8211; \\sqrt {20} \\).<\/blockquote>\n<\/li>\n<\/ul>\n<blockquote>\n<p>Determina o n\u00famero que corresponde ao ponto E.<br \/>Mostra como chegaste \u00e0 tua resposta.<\/p>\n<\/blockquote>\n<p>\u00a0<\/p>\n<p>Aplicando o Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo [ACD], vem:<\/p>\n<p>\\[\\overline {AC} = \\sqrt {{{\\overline {AD} }^2} + {{\\overline {CD} }^2}} = \\sqrt {{4^2} + {2^2}} = \\sqrt {16 + 4} = \\sqrt {20} \\]<\/p>\n<p>Assim, e como a abcissa do ponto A \u00e9 \\({x_A} = 1 &#8211; \\sqrt {20} \\), ent\u00e3o a abcissa do ponto E,\u00a0 ser\u00e1 \\[{x_E} = {x_A} + \\sqrt {20} = 1 &#8211; \\sqrt {20} + \\sqrt {20} = 1\\]<\/p>\n<p>Portanto, \\(E \\to 1\\).<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23681' onClick='GTTabs_show(0,23681)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura, est\u00e1 representado um ret\u00e2ngulo [ABCD].Os v\u00e9rtices A e D s\u00e3o pontos da reta real. Sabe-se ainda que: o ponto E \u00e9 um ponto da reta real; \\(\\overline {AB} =&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":23683,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,682],"tags":[424,67,265,118],"series":[],"class_list":["post-23681","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-teorema-de-pitagoras","tag-8-o-ano","tag-geometria","tag-reta-real","tag-teorema-de-pitagoras"],"views":233,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-3_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23681","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=23681"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23681\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/23683"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23681"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23681"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23681"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=23681"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}