{"id":3351,"date":"2010-10-03T15:09:54","date_gmt":"2010-10-03T14:09:54","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=3351"},"modified":"2022-01-18T21:55:11","modified_gmt":"2022-01-18T21:55:11","slug":"quadrado-e-rectangulo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=3351","title":{"rendered":"Quadrado e ret\u00e2ngulo"},"content":{"rendered":"<p><ul id='GTTabs_ul_3351' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_3351' class='GTTabs_curr'><a  id=\"3351_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_3351' ><a  id=\"3351_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_3351'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/qrect.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"3513\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=3513\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/qrect.jpg\" data-orig-size=\"567,352\" 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=\"Quadrados e rect\u00e2ngulos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/qrect.jpg\" class=\"alignright size-thumbnail wp-image-3513\" title=\"Quadrados e rect\u00e2ngulos\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/qrect-150x150.jpg\" alt=\"\" width=\"150\" height=\"150\" \/><\/a>Considera um quadrado de lado $2x$ e um ret\u00e2ngulo de dimens\u00f5es $x$ e $x+4$.<\/p>\n<p>Para que valores de $x$ as duas figuras t\u00eam o mesmo per\u00edmetro?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_3351' onClick='GTTabs_show(1,3351)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_3351'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><!--more--><\/p>\n<ul>\n<li>\n<blockquote>\n<p>Recorda: ${{P}_{Q}}=4\\times l$ e ${{P}_{R}}=2\\times l+2\\times c=2\\times (l+c)$<\/p>\n<\/blockquote>\n<\/li>\n<\/ul>\n<p>O per\u00edmetro do quadrado pode ser expresso por: ${{P}_{Q}}=4\\times (2x)$.<\/p>\n<p>O per\u00edmetro do ret\u00e2ngulo pode ser expresso por: ${{P}_{R}}=2\\times x+2\\times (x+4)$.<\/p>\n<p>Logo, o problema pode ser equacionado por: \\[4\\times (2x)=2x+2\\times (x+4)\\]<\/p>\n<p>Resolvendo a equa\u00e7\u00e3o, vem: \\[\\begin{array}{*{35}{l}}<br \/>\n4\\times (2x)=2x+2\\times (x+4) &amp; \\Leftrightarrow\u00a0 &amp; 8x=2x+2x+8\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 8x-4x=8\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 4x=8\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x=2\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>As duas figuras t\u00eam o mesmo per\u00edmetro para $x=2$.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_3351' onClick='GTTabs_show(0,3351)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera um quadrado de lado $2x$ e um ret\u00e2ngulo de dimens\u00f5es $x$ e $x+4$. Para que valores de $x$ as duas figuras t\u00eam o mesmo per\u00edmetro? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20608,"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-3351","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":1228,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/7V2Pag066-9_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3351","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=3351"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3351\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20608"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3351"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3351"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3351"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=3351"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}