{"id":23450,"date":"2022-12-08T02:04:38","date_gmt":"2022-12-08T02:04:38","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=23450"},"modified":"2022-12-27T23:52:54","modified_gmt":"2022-12-27T23:52:54","slug":"calcula-o-valor-de-x-c","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=23450","title":{"rendered":"Calcula o valor de x (C)"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_23450' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_23450' class='GTTabs_curr'><a  id=\"23450_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_23450' ><a  id=\"23450_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_23450'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Calcula o valor de x (unidade de comprimento: cm):<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag064-1C.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23435\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23435\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag064-1C.png\" data-orig-size=\"340,195\" 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_Pag064-1C\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag064-1C.png\" class=\"aligncenter wp-image-23435 size-medium\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag064-1C-300x172.png\" alt=\"\" width=\"300\" height=\"172\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag064-1C-300x172.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag064-1C.png 340w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23450' onClick='GTTabs_show(1,23450)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_23450'>\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_Pag064-1C_ang_letras.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23443\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23443\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag064-1C_ang_letras.png\" data-orig-size=\"340,195\" 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_Pag064-1C_ang_letras\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag064-1C_ang_letras.png\" class=\"aligncenter wp-image-23443 size-medium\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag064-1C_ang_letras-300x172.png\" alt=\"\" width=\"300\" height=\"172\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag064-1C_ang_letras-300x172.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag064-1C_ang_letras.png 340w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<h6>Alternativa 1<\/h6>\n<p>Por aplica\u00e7\u00e3o do Teorema de Pit\u00e1goras no tri\u00e2ngulo [ABC], vem:<\/p>\n<p>\\[\\overline {AC} = \\sqrt {{{\\overline {AB} }^2} + {{\\overline {BC} }^2}} = \\sqrt {{8^2} + {6^2}} = \\sqrt {64 + 36} = \\sqrt {100} = 10\\]<\/p>\n<p>Portanto, \\(\\overline {AC} = 10\\) cm.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag064-1C_ang_letras.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23443\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23443\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag064-1C_ang_letras.png\" data-orig-size=\"340,195\" 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_Pag064-1C_ang_letras\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag064-1C_ang_letras.png\" class=\"aligncenter wp-image-23443 size-medium\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag064-1C_ang_letras-300x172.png\" alt=\"\" width=\"300\" height=\"172\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag064-1C_ang_letras-300x172.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag064-1C_ang_letras.png 340w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<h6>Alternativa 2<\/h6>\n<p>Consideremos os tri\u00e2ngulos [ABC] e [ABH].<\/p>\n<p>Como os tri\u00e2ngulos [ABC] e [ABH] s\u00e3o semelhantes (crit\u00e9rio AA), os comprimentos dos lados correspondentes s\u00e3o diretamente proporcionais:<\/p>\n<p>\\[\\frac{{\\overline {AC} }}{{\\overline {AB} }} = \\frac{{\\overline {BC} }}{{\\overline {BH} }} = \\frac{{\\overline {AB} }}{{\\overline {AH} }}\\]<\/p>\n<p><strong>Nota<\/strong>:<br \/>Os lados correspondentes, nos dois tri\u00e2ngulos, s\u00e3o os lados que se op\u00f5em aos \u00e2ngulos marcados com a mesma cor.<\/p>\n<p>Considerando as duas primeiras raz\u00f5es e substituindo os valores conhecidos, temos:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\frac{{\\overline {AC} }}{8} = \\frac{6}{{4,8}}}&amp; \\Leftrightarrow &amp;{4,8 \\times \\overline {AC} = 8 \\times 6}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {AC} = \\frac{{8 \\times 6}}{{4,8}}}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {AC} = 10}\\end{array}\\]<\/p>\n<p>Portanto, \\(\\overline {AC} = 10\\) cm.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23450' onClick='GTTabs_show(0,23450)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Calcula o valor de x (unidade de comprimento: cm): Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":23436,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,682],"tags":[424,67,149,118],"series":[],"class_list":["post-23450","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-semelhanca-de-triangulos","tag-teorema-de-pitagoras"],"views":215,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag064-1C_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23450","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=23450"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23450\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/23436"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23450"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23450"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23450"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=23450"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}