{"id":8437,"date":"2012-04-17T18:20:23","date_gmt":"2012-04-17T17:20:23","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=8437"},"modified":"2022-01-29T23:33:21","modified_gmt":"2022-01-29T23:33:21","slug":"uma-folha-dobrada","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=8437","title":{"rendered":"Uma folha dobrada"},"content":{"rendered":"<p><ul id='GTTabs_ul_8437' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_8437' class='GTTabs_curr'><a  id=\"8437_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_8437' ><a  id=\"8437_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_8437'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag125-1aa.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"8439\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=8439\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag125-1aa.jpg\" data-orig-size=\"343,197\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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;}\" data-image-title=\"Folha de papel\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag125-1aa.jpg\" class=\"alignright wp-image-8439\" title=\"Folha de papel\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag125-1aa.jpg\" alt=\"\" width=\"270\" height=\"155\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag125-1aa.jpg 343w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag125-1aa-300x172.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag125-1aa-150x86.jpg 150w\" sizes=\"auto, (max-width: 270px) 100vw, 270px\" \/><\/a>Depois de dobrada uma folha de papel retangular, o v\u00e9rtice A coincide com o v\u00e9rtice C.<\/p>\n<p>Calcule o comprimento do vinco, sabendo que $\\overline {AB}\u00a0 = 24\\,cm$ e $\\overline {AD}\u00a0 = 18\\,cm$.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8437' onClick='GTTabs_show(1,8437)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_8437'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--> <img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"8441\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=8441\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag125-1.png\" data-orig-size=\"616,182\" 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;}\" data-image-title=\"Foha dobrada\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag125-1.png\" class=\"aligncenter wp-image-8441 size-full\" title=\"Foha dobrada\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag125-1.png\" alt=\"\" width=\"616\" height=\"182\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag125-1.png 616w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag125-1-300x88.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag125-1-150x44.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag125-1-400x118.png 400w\" sizes=\"auto, (max-width: 616px) 100vw, 616px\" \/>Ao dobrar a folha fazendo coincidir os pontos A e C, verifica-se a sobreposi\u00e7\u00e3o dos segmentos [AF] e [CF], quer de [AE] e [CE]. Assim, o ponto F \u00e9 equidistante dos pontos A e C; e o ponto E \u00e9 equidistante dos pontos A e C. Consequentemente, a reta EF \u00e9 a mediatriz da diagonal [AC] do ret\u00e2ngulo [ABCD].<\/p>\n<p>Ora, $$\\operatorname{tg} E\\widehat AO = \\frac{{\\overline {BC} }}{{\\overline {AB} }} = \\frac{{\\overline {EO} }}{{\\overline {AO} }} = \\frac{{18}}{{24}} = \\frac{3}{4}$$<\/p>\n<p>Por outro lado, $$\\overline {AO}\u00a0 = \\frac{1}{2}\\overline {AC}\u00a0 = \\frac{1}{2}\\sqrt {{{18}^2} + {{24}^2}}\u00a0 = \\frac{1}{2} \\times 30 = 15$$ Logo, $$\\overline {EF}\u00a0 = 2 \\times \\overline {EO}\u00a0 = 2 \\times \\frac{3}{4} \\times \\overline {AO}\u00a0 = 2 \\times \\frac{3}{4} \\times 15 = 22,5$$<\/p>\n<p>Portanto, o vinco tem 22,5 cent\u00edmetros de comprimento.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8437' onClick='GTTabs_show(0,8437)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Depois de dobrada uma folha de papel retangular, o v\u00e9rtice A coincide com o v\u00e9rtice C. Calcule o comprimento do vinco, sabendo que $\\overline {AB}\u00a0 = 24\\,cm$ e $\\overline {AD}\u00a0 =&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21090,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,295],"tags":[427,300],"series":[],"class_list":["post-8437","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-aplicando","category-funcoes-seno-co-seno-e-tangente","tag-12-o-ano","tag-funcao-tangente"],"views":3105,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12V3Pag125-1_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8437","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=8437"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8437\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21090"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8437"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8437"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8437"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=8437"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}