{"id":23518,"date":"2022-12-08T22:07:00","date_gmt":"2022-12-08T22:07:00","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=23518"},"modified":"2022-12-27T23:56:02","modified_gmt":"2022-12-27T23:56:02","slug":"o-perimetro-de-um-triangulo-retangulo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=23518","title":{"rendered":"O per\u00edmetro de um tri\u00e2ngulo ret\u00e2ngulo"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_23518' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_23518' class='GTTabs_curr'><a  id=\"23518_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_23518' ><a  id=\"23518_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_23518'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considera o seguinte tri\u00e2ngulo ret\u00e2ngulo.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-11.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23519\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23519\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-11.png\" data-orig-size=\"346,188\" 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_Pag066-11\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-11.png\" class=\"aligncenter wp-image-23519 size-medium\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-11-300x163.png\" alt=\"\" width=\"300\" height=\"163\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-11-300x163.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-11.png 346w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>A \u00e1rea do tri\u00e2ngulo \u00e9 54 cm<sup>2<\/sup>.<br \/>Determina o valor exato do seu per\u00edmetro.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23518' onClick='GTTabs_show(1,23518)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_23518'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-11_Letras.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23521\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23521\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-11_Letras.png\" data-orig-size=\"346,188\" 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_Pag066-11_Letras\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-11_Letras.png\" class=\"aligncenter wp-image-23521 size-medium\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-11_Letras-300x163.png\" alt=\"\" width=\"300\" height=\"163\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-11_Letras-300x163.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-11_Letras.png 346w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>\u00a0<\/p>\n<p>Como a \u00e1rea do tri\u00e2ngulo \u00e9 54 cm<sup>2<\/sup>, temos:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\frac{{\\overline {AB} \\times \\overline {BC} }}{2} = 54}&amp; \\Leftrightarrow &amp;{\\frac{{12 \\times \\overline {BC} }}{2} = 54}\\\\{}&amp; \\Leftrightarrow &amp;{6 \\times \\overline {BC} = 54}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {BC} = 9}\\end{array}\\]<\/p>\n<p>Assim, o tri\u00e2ngulo tem \\[P = \\overline {AB} + \\overline {BC} + \\overline {AC} = 12 + 9 + \\sqrt {{{12}^2} + {9^2}} = 21 + \\sqrt {225} = 21 + 15 = 36\\] cent\u00edmetros de per\u00edmetro.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23518' onClick='GTTabs_show(0,23518)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera o seguinte tri\u00e2ngulo ret\u00e2ngulo. A \u00e1rea do tri\u00e2ngulo \u00e9 54 cm2.Determina o valor exato do seu per\u00edmetro. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":23520,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,682],"tags":[424,67,118],"series":[],"class_list":["post-23518","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-teorema-de-pitagoras"],"views":209,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-11_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23518","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=23518"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23518\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/23520"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23518"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23518"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23518"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=23518"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}