{"id":24837,"date":"2023-04-04T17:20:00","date_gmt":"2023-04-04T16:20:00","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24837"},"modified":"2023-04-04T22:30:30","modified_gmt":"2023-04-04T21:30:30","slug":"azulejos-dispostos-em-forma-de-quadrado","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24837","title":{"rendered":"Azulejos dispostos em forma de quadrado"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24837' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24837' class='GTTabs_curr'><a  id=\"24837_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24837' ><a  id=\"24837_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_24837'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Queremos dispor em forma de quadrado v\u00e1rios azulejos que temos, de forma tamb\u00e9m quadrada.<\/p>\n<p>Experiment\u00e1mos de duas maneiras.<br \/>Da primeira vez sobraram 39.<br \/>Acrescent\u00e1mos 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_24837' onClick='GTTabs_show(1,24837)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24837'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Queremos dispor em forma de quadrado v\u00e1rios azulejos que temos, de forma tamb\u00e9m quadrada.<\/p>\n<p>Experiment\u00e1mos de duas maneiras.<br \/>Da primeira vez sobraram 39.<br \/>Acrescent\u00e1mos mais um azulejo de cada lado. Desta vez faltaram 50.<\/p>\n<p>De quantos azulejos disp\u00fanhamos inicialmente?<\/p>\n<\/blockquote>\n<p>\u00a0<\/p>\n<p>1.\u00aa experimenta\u00e7\u00e3o &#8211; N\u00famero total de azulejos : \\(N = {n^2} + 39\\)<\/p>\n<p>2.\u00aa experimenta\u00e7\u00e3o &#8211; N\u00famero total de azulejos: \\(N = {\\left( {n + 1} \\right)^2} &#8211; 50\\)<\/p>\n<p>Equacionando o problema e resolvendo a equa\u00e7\u00e3o, vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{{\\left( {n + 1} \\right)}^2} &#8211; 50 = {n^2} + 39}&amp; \\Leftrightarrow &amp;{{n^2} + 2n + 1 &#8211; 50 = {n^2} + 39}\\\\{}&amp; \\Leftrightarrow &amp;{2n = 49 + 39}\\\\{}&amp; \\Leftrightarrow &amp;{n = 44}\\end{array}\\]<\/p>\n<p>Portanto, disp\u00fanhamos inicialmente de \\(N = {44^2} + 39 = 1975\\) azulejos.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24837' onClick='GTTabs_show(0,24837)'>&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 que temos, de forma tamb\u00e9m quadrada. Experiment\u00e1mos de duas maneiras.Da primeira vez sobraram 39.Acrescent\u00e1mos mais um azulejo de cada lado. Desta vez faltaram&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":24839,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[100,97,700],"tags":[424,706,198],"series":[],"class_list":["post-24837","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-monomios-e-polinomios","tag-8-o-ano","tag-equacao-incompleta-do-2-o-grau","tag-lei-do-anulamento-do-produto"],"views":69,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag149-22_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24837","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=24837"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24837\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/24839"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24837"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24837"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24837"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24837"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}