{"id":25610,"date":"2023-05-06T18:26:08","date_gmt":"2023-05-06T17:26:08","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=25610"},"modified":"2023-05-07T22:55:57","modified_gmt":"2023-05-07T21:55:57","slug":"um-quadrado-3","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=25610","title":{"rendered":"Um quadrado"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_25610' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_25610' class='GTTabs_curr'><a  id=\"25610_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_25610' ><a  id=\"25610_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_25610'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Um quadrado, de lado <em>x<\/em>, tem per\u00edmetro <em>p<\/em> e \u00e1rea <em>a<\/em> (<em>p<\/em>&gt;0 e <em>a<\/em>&gt;0).<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T6_Quadrado.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25611\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25611\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T6_Quadrado.png\" data-orig-size=\"715,691\" 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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag189-T6_Quadrado\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T6_Quadrado.png\" class=\"aligncenter wp-image-25611\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T6_Quadrado-300x290.png\" alt=\"\" width=\"240\" height=\"232\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T6_Quadrado-300x290.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T6_Quadrado.png 715w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a><\/p>\n<ol>\n<li>Escreve uma igualdade que relacione <em>x<\/em> e <em>p<\/em> e outra que relacione <em>x<\/em> e a.<\/li>\n<li>Resolve cada uma das equa\u00e7\u00f5es em ordem a <em>x<\/em> e deduz que \\({p^2} = 16a\\).<\/li>\n<li>Existe algum quadrado de per\u00edmetro 20 cm e de \u00e1rea 24 cm<sup>2<\/sup>?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_25610' onClick='GTTabs_show(1,25610)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_25610'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Um quadrado, de lado <em>x<\/em>, tem per\u00edmetro <em>p<\/em> e \u00e1rea <em>a<\/em> (<em>p<\/em>&gt;0 e <em>a<\/em>&gt;0).<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T6_Quadrado.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25611\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25611\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T6_Quadrado.png\" data-orig-size=\"715,691\" 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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag189-T6_Quadrado\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T6_Quadrado.png\" class=\"aligncenter wp-image-25611\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T6_Quadrado-300x290.png\" alt=\"\" width=\"240\" height=\"232\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T6_Quadrado-300x290.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag189-T6_Quadrado.png 715w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a><\/p>\n<ol>\n<li>\n<blockquote>Escreve uma igualdade que relacione <em>x<\/em> e <em>p<\/em> e outra que relacione <em>x<\/em> e a.<\/blockquote>\n<\/li>\n<li>\n<blockquote>Resolve cada uma das equa\u00e7\u00f5es em ordem a <em>x<\/em> e deduz que \\({p^2} = 16a\\).<\/blockquote>\n<\/li>\n<li>\n<blockquote>Existe algum quadrado de per\u00edmetro 20 cm e de \u00e1rea 24 cm<sup>2<\/sup>?<\/blockquote>\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ol>\n<li>\\(p = 4x\\) \u00e9 uma igualdade que relaciona <em>x<\/em> e <em>p<\/em>.<br \/>E \\(a = {x^2}\\) \u00e9 uma igualdade que relaciona <em>x<\/em> e a.<br \/><br \/><\/li>\n<li>Tendo em considera\u00e7\u00e3o que <em>p<\/em>&gt;0, <em>a<\/em>&gt;0 e <em>x<\/em>&gt;0, vem:<br \/>\\[\\begin{array}{*{20}{c}}{\\begin{array}{*{20}{l}}{p = 4x}&amp; \\Leftrightarrow &amp;{x = \\frac{p}{4}}\\end{array}}&amp;{}&amp;{\\rm{e}}&amp;{}&amp;{\\begin{array}{*{20}{l}}{a = {x^2}}&amp; \\Leftrightarrow &amp;{x = \\sqrt a }\\end{array}}\\end{array}\\]<br \/>Donde se conclui que \\(\\begin{array}{*{20}{l}}{p = 4x}&amp; \\Leftrightarrow &amp;{p = 4\\sqrt a }\\end{array}\\).<br \/>Logo, \\({p^2} = {\\left( {4\\sqrt a } \\right)^2} = 16a\\).<br \/><br \/><\/li>\n<li>Ora, \\({20^2} = 400\\) e \\(24 \\times 16 = 384\\).<br \/>Como \\(400 \\ne 384\\), ent\u00e3o n\u00e3o existe qualquer quadrado de per\u00edmetro 20 cm e de \u00e1rea 24 cm<sup>2<\/sup>.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_25610' onClick='GTTabs_show(0,25610)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um quadrado, de lado x, tem per\u00edmetro p e \u00e1rea a (p&gt;0 e a&gt;0). Escreve uma igualdade que relacione x e p e outra que relacione x e a. Resolve cada&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19189,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,714],"tags":[424,192],"series":[],"class_list":["post-25610","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-literais-e-sistemas","tag-8-o-ano","tag-equacoes-literais"],"views":78,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat75.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25610","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=25610"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25610\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19189"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=25610"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=25610"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=25610"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=25610"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}