{"id":23665,"date":"2022-12-10T21:38:30","date_gmt":"2022-12-10T21:38:30","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=23665"},"modified":"2022-12-20T00:31:53","modified_gmt":"2022-12-20T00:31:53","slug":"uma-viga-do-telhado","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=23665","title":{"rendered":"Uma viga do telhado"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_23665' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_23665' class='GTTabs_curr'><a  id=\"23665_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_23665' ><a  id=\"23665_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_23665'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>A viga, a vermelho, do telhado da casa seguinte precisa de ser mudada.<br \/>De acordo com as indica\u00e7\u00f5es da figura, qual deve ser o comprimento dessa viga, arredondado \u00e0s mil\u00e9simas?<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23666\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23666\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-1.png\" data-orig-size=\"385,302\" 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_Pag070-1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-1.png\" class=\"aligncenter wp-image-23666\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-1-300x235.png\" alt=\"\" width=\"300\" height=\"235\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-1-300x235.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-1.png 385w\" 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_23665' onClick='GTTabs_show(1,23665)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_23665'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>A viga, a vermelho, do telhado da casa seguinte precisa de ser mudada.<br \/>De acordo com as indica\u00e7\u00f5es da figura, qual deve ser o comprimento dessa viga, arredondado \u00e0s mil\u00e9simas?<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-1_Pontos-Angulos.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23669\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23669\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-1_Pontos-Angulos.png\" data-orig-size=\"385,302\" 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_Pag070-1_Pontos-Angulos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-1_Pontos-Angulos.png\" class=\"aligncenter wp-image-23669\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-1_Pontos-Angulos-300x235.png\" alt=\"\" width=\"300\" height=\"235\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-1_Pontos-Angulos-300x235.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag070-1_Pontos-Angulos.png 385w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<\/blockquote>\n<p>\u00a0<\/p>\n<p>Como os tri\u00e2ngulos[ABH] e [BCH] s\u00e3o semelhantes (crit\u00e9rio AA), ent\u00e3o os comprimentos dos lados correspondentes s\u00e3o diretamente proporcionais:<\/p>\n<p>\\[\\frac{{\\overline {BH} }}{{\\overline {CH} }} = \\frac{{\\overline {AH} }}{{\\overline {BH} }} = \\frac{{\\overline {AB} }}{{\\overline {BC} }}\\]<\/p>\n<p>Considerando as duas primeiras raz\u00f5es e substituindo os valores conhecidos, vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\frac{{\\overline {BH} }}{3} = \\frac{1}{{\\overline {BH} }}}&amp; \\Leftrightarrow &amp;{\\overline {BH} \\times \\overline {BH} = 3 \\times 1}\\\\{}&amp; \\Leftrightarrow &amp;{{{\\overline {BH} }^2} = 3}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {BH} = \\sqrt 3 }\\end{array}\\]<\/p>\n<p>A viga a substituir deve ter \\(\\overline {BH} = \\sqrt 3 \\approx 1,732\\) metros de comprimento.<\/p>\n<p>\u00a0<\/p>\n<h6>Uma vers\u00e3o ilustrada<\/h6>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/IMG_prob_v4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23755\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23755\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/IMG_prob_v4.png\" data-orig-size=\"2791,2259\" 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=\"IMG_prob_v4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/IMG_prob_v4-1024x829.png\" class=\"aligncenter wp-image-23755 size-full\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/IMG_prob_v4.png\" alt=\"\" width=\"2791\" height=\"2259\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/IMG_prob_v4.png 2791w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/IMG_prob_v4-300x243.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/IMG_prob_v4-1024x829.png 1024w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/IMG_prob_v4-768x622.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/IMG_prob_v4-1536x1243.png 1536w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/IMG_prob_v4-2048x1658.png 2048w\" sizes=\"auto, (max-width: 2791px) 100vw, 2791px\" \/><\/a><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23665' onClick='GTTabs_show(0,23665)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A viga, a vermelho, do telhado da casa seguinte precisa de ser mudada.De acordo com as indica\u00e7\u00f5es da figura, qual deve ser o comprimento dessa viga, arredondado \u00e0s mil\u00e9simas? Resolu\u00e7\u00e3o &gt;&gt;&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":23755,"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],"series":[],"class_list":["post-23665","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"],"views":281,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/IMG_prob_v4.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23665","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=23665"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23665\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/23755"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23665"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23665"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23665"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=23665"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}