{"id":12834,"date":"2017-10-29T12:54:51","date_gmt":"2017-10-29T12:54:51","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=12834"},"modified":"2022-01-15T23:36:03","modified_gmt":"2022-01-15T23:36:03","slug":"substituir-paineis-retangulares","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=12834","title":{"rendered":"Substituir pain\u00e9is retangulares"},"content":{"rendered":"<p><ul id='GTTabs_ul_12834' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_12834' class='GTTabs_curr'><a  id=\"12834_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_12834' ><a  id=\"12834_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_12834'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Paineis.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"12840\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=12840\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Paineis.png\" data-orig-size=\"536,343\" 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=\"Pain\u00e9is\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Paineis.png\" class=\"alignright wp-image-12840 size-medium\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Paineis-300x192.png\" alt=\"\" width=\"300\" height=\"192\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Paineis-300x192.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Paineis.png 536w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Pretende-se substituir pain\u00e9is retangulares de dimens\u00f5es 2,5 m e 3,5 m por pain\u00e9is quadrados que tenham a mesma \u00e1rea.<\/p>\n<p>Determina, com erro inferior a 1 dm e utilizando a tabela de quadrados perfeitos abaixo, dois valores aproximados, um por defeito e outro por excesso, da medida, em metros, do lado de cada um desses quadrados.<\/p>\n<table style=\"width: 60%;\">\n<tbody>\n<tr>\n<td>\\(x\\)<\/td>\n<td>26<\/td>\n<td>27<\/td>\n<td>28<\/td>\n<td>29<\/td>\n<td>30<\/td>\n<td>31<\/td>\n<td>32<\/td>\n<td>33<\/td>\n<td>34<\/td>\n<\/tr>\n<tr>\n<td>\\({x^2}\\)<\/td>\n<td>676<\/td>\n<td>729<\/td>\n<td>784<\/td>\n<td>841<\/td>\n<td>900<\/td>\n<td>961<\/td>\n<td>1024<\/td>\n<td>1089<\/td>\n<td>1156<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_12834' onClick='GTTabs_show(1,12834)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_12834'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><!--more--><\/p>\n<p>Os pain\u00e9is retangulares t\u00eam de \u00e1rea\u00a0\\(A = 2,5 \\times 3,5 = 8,75\\) m<sup>2<\/sup>, ou seja,\u00a0\\(875\\) dm<sup>2<\/sup>.<\/p>\n<p>Trabalhando a \u00e1rea em dec\u00edmetros quadrados e os comprimentos em dec\u00edmetros, tem-se\u00a0\\(x = \\sqrt {875} \\) e\u00a0\\(r = 1\\). Logo,\u00a0\\(n = 1\\).<\/p>\n<p>Assim, vem sucessivamente:<\/p>\n<p>\\[\\begin{array}{*{20}{c}}{841 &lt; {1^2} \\times 875 &lt; 900}\\\\{{{\\left( {\\frac{{29}}{1}} \\right)}^2} &lt; 875 &lt; {{\\left( {\\frac{{30}}{1}} \\right)}^2}}\\\\{29 &lt; \\sqrt {875} &lt; 30}\\end{array}\\]<\/p>\n<p>Portanto, os valores pedidos s\u00e3o 2,9 m e 3,0 m, respetivamente.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_12834' onClick='GTTabs_show(0,12834)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Pretende-se substituir pain\u00e9is retangulares de dimens\u00f5es 2,5 m e 3,5 m por pain\u00e9is quadrados que tenham a mesma \u00e1rea. Determina, com erro inferior a 1 dm e utilizando a tabela de&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20311,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,258],"tags":[443,444,442],"series":[],"class_list":["post-12834","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-os-numeros-reais","tag-enquadramento","tag-erro","tag-valor-aproximado"],"views":2095,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/9V1Pag024-9_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12834","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=12834"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12834\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20311"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12834"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12834"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12834"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=12834"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}