{"id":12890,"date":"2017-10-30T18:55:40","date_gmt":"2017-10-30T18:55:40","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=12890"},"modified":"2022-01-16T00:00:44","modified_gmt":"2022-01-16T00:00:44","slug":"observa-o-retangulo-abcd-da-figura","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=12890","title":{"rendered":"Observa o ret\u00e2ngulo [ABCD] da figura"},"content":{"rendered":"<p><ul id='GTTabs_ul_12890' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_12890' class='GTTabs_curr'><a  id=\"12890_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_12890' ><a  id=\"12890_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_12890'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Retangulo.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"12891\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=12891\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Retangulo.png\" data-orig-size=\"367,208\" 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=\"Ret\u00e2ngulo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Retangulo.png\" class=\"alignright wp-image-12891\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Retangulo-300x170.png\" alt=\"\" width=\"240\" height=\"136\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Retangulo-300x170.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Retangulo.png 367w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>Observa o ret\u00e2ngulo [ABCD] da figura.<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Determina o valor exato do per\u00edmetro do ret\u00e2ngulo [ABCD].<\/li>\n<li>Aproxima o valor da diagonal do ret\u00e2ngulo [ABCD] \u00e0s cent\u00e9simas.<\/li>\n<li>Qual \u00e9 o valor exato da \u00e1rea do ret\u00e2ngulo [ABCD]?<br \/>\nDetermina um intervalo de extremos racionais e de medida de comprimento inferior ou igual a\u00a0\\({\\frac{1}{2}}\\) e que contenha essa \u00e1rea.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_12890' onClick='GTTabs_show(1,12890)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_12890'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Retangulo.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"12891\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=12891\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Retangulo.png\" data-orig-size=\"367,208\" 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=\"Ret\u00e2ngulo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Retangulo.png\" class=\"alignright wp-image-12891\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Retangulo.png\" alt=\"\" width=\"240\" height=\"136\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Retangulo.png 367w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Retangulo-300x170.png 300w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>O per\u00edmetro do ret\u00e2ngulo da figura \u00e9\u00a0\\({P_{\\left[ {ABCD} \\right]}} = 2 \\times \\left( {\\sqrt 3 + \\sqrt {11} } \\right)\\) cm.<\/li>\n<li>Aplicando o Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo [ACD], temos: \\(\\overline {AC} = \\sqrt {{{\\overline {AD} }^2} + {{\\overline {CD} }^2}} = \\sqrt {{{\\left( {\\sqrt 3 } \\right)}^2} + {{\\left( {\\sqrt {11} } \\right)}^2}} = \\sqrt {3 + 11} = \\sqrt {14} \\) cm.\n<p>Utilizando o m\u00e9todo dos quadrados perfeitos, obt\u00e9m-se o seguinte enquadramento:<br \/>\n\\[\\begin{array}{*{20}{c}}{{{374}^2} &lt; {{100}^2} \\times 14 &lt; {{375}^2}}\\\\{{{\\left( {\\frac{{374}}{{100}}} \\right)}^2} &lt; 14 &lt; {{\\left( {\\frac{{375}}{{100}}} \\right)}^2}}\\\\{3,74 &lt; \\sqrt {14} &lt; 3,75}\\end{array}\\]<br \/>\nLogo,\u00a0\\(3,74\\;cm &lt; \\overline {AC} &lt; 3,75\\;cm\\).<br \/>\nComo\u00a0\\(\\left| {{{3,74}^2} &#8211; 14} \\right| = 0,0124\\) e\u00a0\\(\\left| {{{3,75}^2} &#8211; 14} \\right| = 0,0625\\), ent\u00e3o\u00a0\\(\\overline {AC} \\approx 3,74\\;cm\\), com aproxima\u00e7\u00e3o \u00e0s cent\u00e9simas.<\/p>\n<\/li>\n<li>A \u00e1rea do ret\u00e2ngulo [ABCD] \u00e9\u00a0\\({A_{\\left[ {ABCD} \\right]}} = \\overline {AB} \\times \\overline {BC} = \\sqrt {11} \\times \\sqrt 3 = \\sqrt {33} \\) cm<sup>2<\/sup>.\n<p>Utilizando novamente o m\u00e9todo dos quadrados perfeitos, obt\u00e9m-se o seguinte enquadramento:<br \/>\n\\[\\begin{array}{*{20}{c}}{121 &lt; {2^2} \\times 33 &lt; 144}\\\\{{{11}^2} &lt; {2^2} \\times 33 &lt; {{12}^2}}\\\\{{{\\left( {\\frac{{11}}{2}} \\right)}^2} &lt; 33 &lt; {{\\left( {\\frac{{12}}{2}} \\right)}^2}}\\\\{5,5 &lt; \\sqrt {33} &lt; 6,0}\\end{array}\\]<br \/>\nPortanto,\u00a0\\({A_{\\left[ {ABCD} \\right]}} \\in \\left] {5,5;\\;6,0} \\right[\\), em cent\u00edmetros quadrados.<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_12890' onClick='GTTabs_show(0,12890)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Observa o ret\u00e2ngulo [ABCD] da figura. Determina o valor exato do per\u00edmetro do ret\u00e2ngulo [ABCD]. Aproxima o valor da diagonal do ret\u00e2ngulo [ABCD] \u00e0s cent\u00e9simas. Qual \u00e9 o valor exato da&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20318,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,258],"tags":[443,442],"series":[],"class_list":["post-12890","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-os-numeros-reais","tag-enquadramento","tag-valor-aproximado"],"views":1517,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/9V1Pag035-5_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12890","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=12890"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12890\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20318"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12890"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12890"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12890"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=12890"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}