{"id":3394,"date":"2010-10-03T16:10:23","date_gmt":"2010-10-03T15:10:23","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=3394"},"modified":"2022-01-18T22:23:33","modified_gmt":"2022-01-18T22:23:33","slug":"o-desenho-da-ana","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=3394","title":{"rendered":"O desenho da Ana"},"content":{"rendered":"<p><ul id='GTTabs_ul_3394' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_3394' class='GTTabs_curr'><a  id=\"3394_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_3394' ><a  id=\"3394_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_3394'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/desenhoana.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"3399\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=3399\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/desenhoana.jpg\" data-orig-size=\"483,331\" 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=\"O desenho da Ana\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/desenhoana.jpg\" class=\"alignright wp-image-3399\" title=\"O desenho da Ana\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/desenhoana.jpg\" alt=\"\" width=\"340\" height=\"233\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/desenhoana.jpg 483w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/desenhoana-300x205.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/desenhoana-150x102.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/desenhoana-400x274.jpg 400w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/a>A Ana fez este desenho \u00e0 m\u00e3o e com pouco rigor.<\/p>\n<p>Todas as dimens\u00f5es est\u00e3o expressas em cent\u00edmetros.<\/p>\n<p>Qual \u00e9 o valor de $x$? Pensas que a Ana cometeu um erro? Porqu\u00ea?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_3394' onClick='GTTabs_show(1,3394)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_3394'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"3399\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=3399\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/desenhoana.jpg\" data-orig-size=\"483,331\" 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=\"O desenho da Ana\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/desenhoana.jpg\" class=\"alignright wp-image-3399\" title=\"O desenho da Ana\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/desenhoana.jpg\" alt=\"\" width=\"340\" height=\"233\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/desenhoana.jpg 483w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/desenhoana-300x205.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/desenhoana-150x102.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/desenhoana-400x274.jpg 400w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/>Admitindo que os lados da figura s\u00e3o exclusivamente segmentos de reta horizontais ou verticais, tem-se (porqu\u00ea?): \\[(x+1)+(2x+9)=x+5+2+x\\]<\/p>\n<p>Resolvendo a equa\u00e7\u00e3o, vem: \\[\\begin{array}{*{35}{l}}<br \/>\n(x+1)+(2x+9)=x+5+2+x &amp; \\Leftrightarrow\u00a0 &amp; x+2x+10=2x+7\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 3x-2x=7-10\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x=-3\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>O valor de $x$ que satisfaz as condi\u00e7\u00f5es estabelecidas \u00e9 $-3$.<\/p>\n<p>A Ana ter\u00e1 cometido um erro, pois os comprimentos s\u00e3o n\u00e3o negativos (para $x=-3$, alguns dos comprimentos dos lados da figura seriam negativos).<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_3394' onClick='GTTabs_show(0,3394)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A Ana fez este desenho \u00e0 m\u00e3o e com pouco rigor. Todas as dimens\u00f5es est\u00e3o expressas em cent\u00edmetros. Qual \u00e9 o valor de $x$? Pensas que a Ana cometeu um erro?&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20610,"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-3394","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":1958,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/7V2Pag066-11_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3394","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=3394"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3394\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20610"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3394"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3394"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3394"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=3394"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}