{"id":6886,"date":"2011-05-24T23:18:19","date_gmt":"2011-05-24T22:18:19","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6886"},"modified":"2022-01-18T18:23:49","modified_gmt":"2022-01-18T18:23:49","slug":"o-numero-de-azulejos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6886","title":{"rendered":"O n\u00famero de azulejos"},"content":{"rendered":"<p><ul id='GTTabs_ul_6886' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6886' class='GTTabs_curr'><a  id=\"6886_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6886' ><a  id=\"6886_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_6886'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/azulejos.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6887\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6887\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/azulejos.jpg\" data-orig-size=\"315,315\" 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=\"Azulejos\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/azulejos-300x300.jpg\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/azulejos.jpg\" class=\"alignright size-full wp-image-6887\" title=\"Azulejos\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/azulejos.jpg\" alt=\"\" width=\"151\" height=\"151\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/azulejos.jpg 315w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/azulejos-150x150.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/azulejos-300x300.jpg 300w\" sizes=\"auto, (max-width: 151px) 100vw, 151px\" \/><\/a>Queremos dispor em forma de quadrado v\u00e1rios azulejos, de forma tamb\u00e9m quadrada.<\/p>\n<p>Experiment\u00e1mos de duas maneiras. Da primeira vez sobraram 39. Acrescent\u00e1mos ent\u00e3o mais um azulejo de cada lado. Desta vez faltaram 50.<\/p>\n<p>De quantos azulejos disp\u00fanhamos inicialmente?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6886' onClick='GTTabs_show(1,6886)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6886'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Seja N o n\u00famero de azulejos dispon\u00edveis.<\/p>\n<p>Na primeira vez tent\u00e1mos fazer um quadrado com n azulejos de lado, tendo sobrado 39 azulejos. Assim, temos:<\/p>\n<p>\\[N={{n}^{2}}+39\\]<\/p>\n<p>Na segunda vez tent\u00e1mos fazer um quadrado com n+1 azulejos de lado, tendo faltado 50 azulejos. Assim, temos:<\/p>\n<p>\\[N={{(n+1)}^{2}}-50\\]<\/p>\n<p>Logo, vem:<\/p>\n<p>\\[\\begin{array}{*{35}{l}} \u00a0\u00a0 {{(n+1)}^{2}}-50={{n}^{2}}+39 &amp; \\Leftrightarrow\u00a0 &amp; (n+1)(n+1)-50={{n}^{2}}+39\u00a0 \\\\ \u00a0\u00a0 {} &amp; \\Leftrightarrow\u00a0 &amp; {{n}^{2}}+n+n+1-50={{n}^{2}}+39\u00a0 \\\\ \u00a0\u00a0 {} &amp; \\Leftrightarrow\u00a0 &amp; 2n=88\u00a0 \\\\ \u00a0\u00a0 {} &amp; \\Leftrightarrow\u00a0 &amp; n=44\u00a0 \\\\ \\end{array}\\]<\/p>\n<p>Assim, disp\u00fanhamos inicialmente de $N={{44}^{2}}+39=1975$ azulejos.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6886' onClick='GTTabs_show(0,6886)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Queremos dispor em forma de quadrado v\u00e1rios azulejos, de forma tamb\u00e9m quadrada. Experiment\u00e1mos de duas maneiras. Da primeira vez sobraram 39. Acrescent\u00e1mos ent\u00e3o mais um azulejo de cada lado. Desta vez&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20597,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,193],"tags":[],"series":[],"class_list":["post-6886","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-de-grau-superior-ao-1-"],"views":1711,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/8V2Pag081-5-a_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6886","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=6886"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6886\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20597"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6886"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6886"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6886"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6886"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}