{"id":3368,"date":"2010-10-03T15:37:17","date_gmt":"2010-10-03T14:37:17","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=3368"},"modified":"2022-01-18T22:01:27","modified_gmt":"2022-01-18T22:01:27","slug":"o-perimetro","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=3368","title":{"rendered":"O per\u00edmetro"},"content":{"rendered":"<p><ul id='GTTabs_ul_3368' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_3368' class='GTTabs_curr'><a  id=\"3368_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_3368' ><a  id=\"3368_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_3368'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/figura.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"3372\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=3372\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/figura.jpg\" data-orig-size=\"354,408\" 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=\"Figura\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/figura.jpg\" class=\"alignright wp-image-3372\" title=\"Figura\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/figura.jpg\" alt=\"\" width=\"240\" height=\"277\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/figura.jpg 354w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/figura-260x300.jpg 260w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/figura-130x150.jpg 130w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>Determina $x$ de tal modo que o per\u00edmetro da figura seja 85 cm.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_3368' onClick='GTTabs_show(1,3368)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_3368'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/figura.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"3372\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=3372\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/figura.jpg\" data-orig-size=\"354,408\" 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=\"Figura\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/figura.jpg\" class=\"alignright wp-image-3372\" title=\"Figura\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/figura.jpg\" alt=\"\" width=\"240\" height=\"277\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/figura.jpg 354w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/figura-260x300.jpg 260w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/figura-130x150.jpg 130w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>Partindo do lado superior da figura e rodando no sentido contr\u00e1rio ao dos ponteiros do rel\u00f3gio, o comprimento dos lados do pol\u00edgono (admitindo que os lados consecutivos s\u00e3o perpendiculares) \u00e9 dado por:<\/p>\n<ul>\n<li>$4x+2$<\/li>\n<li>$3x$<\/li>\n<li>$(4x+2)-2x=2x+2$ (Porqu\u00ea?)<\/li>\n<li>$2x$<\/li>\n<li>$2x$<\/li>\n<li>$3x+2x=5x$ (Porqu\u00ea?)<\/li>\n<\/ul>\n<p>Logo, o problema pode ser equacionado por: \\[(4x+2)+3x+(2x+2)+2x+2x+5x=85\\]<\/p>\n<p>Resolvendo a equa\u00e7\u00e3o, vem: \\[\\begin{array}{*{35}{l}}<br \/>\n(4x+2)+3x+(2x+2)+2x+2x+5x=85 &amp; \\Leftrightarrow\u00a0 &amp; 18x=85-4\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; \\frac{18x}{18}=\\frac{81}{18}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x=\\frac{9}{2}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x=4,5\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>Portanto, $x=4,5$ (cm).<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_3368' onClick='GTTabs_show(0,3368)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Determina $x$ de tal modo que o per\u00edmetro da figura seja 85 cm. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20609,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,101],"tags":[424,425],"series":[],"class_list":["post-3368","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes","tag-8-o-ano","tag-equacoes"],"views":2712,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/7V2Pag066-10_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3368","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=3368"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3368\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20609"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3368"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3368"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3368"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=3368"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}