{"id":10116,"date":"2012-10-05T22:45:08","date_gmt":"2012-10-05T21:45:08","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=10116"},"modified":"2022-01-20T22:26:08","modified_gmt":"2022-01-20T22:26:08","slug":"qual-deve-ser-o-valor-de-y","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=10116","title":{"rendered":"Qual deve ser o valor de $y$?"},"content":{"rendered":"<p><ul id='GTTabs_ul_10116' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_10116' class='GTTabs_curr'><a  id=\"10116_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_10116' ><a  id=\"10116_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_10116'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Qual deve ser o valor de $y$ para que a \u00e1rea da figura seja $845$ m<sup>2<\/sup>?<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/dodecagono.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10117\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10117\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/dodecagono.jpg\" data-orig-size=\"294,275\" 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;1349472798&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=\"Dodec\u00e1gono\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/dodecagono.jpg\" class=\"aligncenter  wp-image-10117\" title=\"Dodec\u00e1gono\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/dodecagono.jpg\" alt=\"\" width=\"141\" height=\"132\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/dodecagono.jpg 294w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/dodecagono-150x140.jpg 150w\" sizes=\"auto, (max-width: 141px) 100vw, 141px\" \/><\/a><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10116' onClick='GTTabs_show(1,10116)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_10116'>\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\/dodecagono.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"10117\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=10117\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/dodecagono.jpg\" data-orig-size=\"294,275\" 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;1349472798&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=\"Dodec\u00e1gono\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/dodecagono.jpg\" class=\"aligncenter  wp-image-10117\" title=\"Dodec\u00e1gono\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/dodecagono.jpg\" alt=\"\" width=\"141\" height=\"132\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/dodecagono.jpg 294w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/dodecagono-150x140.jpg 150w\" sizes=\"auto, (max-width: 141px) 100vw, 141px\" \/><\/a><\/p>\n<p>O dodec\u00e1gono pode ser decomposto em $5$ quadrados geometricamente iguais (de que forma?), cuja \u00e1rea individual pode ser expressa por ${y^2}$.<\/p>\n<p>Equacionando o problema e resolvendo a equa\u00e7\u00e3o, temos:<\/p>\n<p>$$\\begin{array}{*{20}{l}} {5{y^2} = 845}&amp; \\Leftrightarrow &amp;{{y^2} = 169}\\\\ {}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}} {y =\u00a0 &#8211; \\sqrt {169} }&amp; \\vee &amp;{y =\u00a0 + \\sqrt {169} } \\end{array}}\\\\ {}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}} {y =\u00a0 &#8211; 13}&amp; \\vee &amp;{y = 13} \\end{array}} \\end{array}$$<\/p>\n<p>Portanto, para que a \u00e1rea da figura seja $845$ m<sup>2<\/sup>, ter\u00e1 de ser ${y = 13}$ m.<br \/>\n(Apenas a solu\u00e7\u00e3o positiva da equa\u00e7\u00e3o \u00e9 solu\u00e7\u00e3o do problema, pois $y$ traduz uma medida de comprimento.)<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10116' onClick='GTTabs_show(0,10116)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Qual deve ser o valor de $y$ para que a \u00e1rea da figura seja $845$ m2? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20784,"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-10116","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":3608,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/10V1Pag037-24_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10116","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=10116"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10116\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20784"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10116"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10116"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10116"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=10116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}