{"id":10127,"date":"2012-10-05T23:02:44","date_gmt":"2012-10-05T22:02:44","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=10127"},"modified":"2022-01-20T22:33:41","modified_gmt":"2022-01-20T22:33:41","slug":"quanto-mede-o-lado-do-quadrado","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=10127","title":{"rendered":"Quanto mede o lado do quadrado?"},"content":{"rendered":"<p><ul id='GTTabs_ul_10127' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_10127' class='GTTabs_curr'><a  id=\"10127_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_10127' ><a  id=\"10127_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_10127'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>\u00a0Quanto mede, com aproxima\u00e7\u00e3o \u00e0s d\u00e9cimas,\u00a0o lado do quadrado, sabendo que a \u00e1rea da parte mais clara \u00e9, aproximadamente, $4,35$ m<sup>2<\/sup>?<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/quadradoquartocirculo.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10131\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10131\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/quadradoquartocirculo.jpg\" data-orig-size=\"273,275\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;AMMA&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1349474736&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=\"Quadrado\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/quadradoquartocirculo.jpg\" class=\"aligncenter  wp-image-10131\" title=\"Quadrado\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/quadradoquartocirculo.jpg\" alt=\"\" width=\"131\" height=\"132\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/quadradoquartocirculo.jpg 273w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/quadradoquartocirculo-150x150.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/quadradoquartocirculo-148x150.jpg 148w\" sizes=\"auto, (max-width: 131px) 100vw, 131px\" \/><\/a><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10127' onClick='GTTabs_show(1,10127)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_10127'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/quadradoquartocirculo.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10131\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10131\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/quadradoquartocirculo.jpg\" data-orig-size=\"273,275\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;AMMA&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1349474736&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=\"Quadrado\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/quadradoquartocirculo.jpg\" class=\"aligncenter  wp-image-10131\" title=\"Quadrado\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/quadradoquartocirculo.jpg\" alt=\"\" width=\"131\" height=\"132\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/quadradoquartocirculo.jpg 273w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/quadradoquartocirculo-150x150.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/quadradoquartocirculo-148x150.jpg 148w\" sizes=\"auto, (max-width: 131px) 100vw, 131px\" \/><\/a><\/p>\n<p>Designado por $r$ o comprimento do lado do quadrado, em metros, temos:<\/p>\n<p>$$\\begin{array}{*{20}{l}} {{A_{Clara}} = 4,35}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}} {{r^2} &#8211; \\frac{1}{4}\\pi\u00a0 \\times {r^2} = 4,35}&amp; \\wedge &amp;{r &gt; 0} \\end{array}}\\\\ {}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}} {4{r^2} &#8211; \\pi\u00a0 \\times {r^2} = 17,4}&amp; \\wedge &amp;{r &gt; 0} \\end{array}}\\\\ {}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}} {\\left( {4 &#8211; \\pi } \\right){r^2} = 17,4}&amp; \\wedge &amp;{r &gt; 0} \\end{array}}\\\\ {}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}} {{r^2} = \\frac{{17,4}}{{4 &#8211; \\pi }}}&amp; \\wedge &amp;{r &gt; 0} \\end{array}}\\\\ {}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}} {r =\u00a0 \\pm \\sqrt {\\frac{{17,4}}{{4 &#8211; \\pi }}} }&amp; \\wedge &amp;{r &gt; 0} \\end{array}}\\\\ {}&amp; \\Leftrightarrow &amp;{r = \\sqrt {\\frac{{17,4}}{{4 &#8211; \\pi }}} } \\end{array}$$<\/p>\n<\/p>\n<p>Portanto, $r \\approx 4,5$ cm.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10127' onClick='GTTabs_show(0,10127)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado \u00a0Quanto mede, com aproxima\u00e7\u00e3o \u00e0s d\u00e9cimas,\u00a0o lado do quadrado, sabendo que a \u00e1rea da parte mais clara \u00e9, aproximadamente, $4,35$ m2? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20785,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[321,97,322],"tags":[429,108,67,430],"series":[],"class_list":["post-10127","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-10-o-ano","category-aplicando","category-modulo-inicial","tag-10-o-ano","tag-area","tag-geometria","tag-modulo-inicial"],"views":2423,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/10V1Pag038-25_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10127","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=10127"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10127\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20785"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10127"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10127"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10127"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=10127"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}