{"id":11363,"date":"2012-11-15T17:18:08","date_gmt":"2012-11-15T17:18:08","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11363"},"modified":"2022-01-20T02:22:40","modified_gmt":"2022-01-20T02:22:40","slug":"o-terreno-da-d-a-antonia","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11363","title":{"rendered":"O terreno da D.\u00aa Ant\u00f3nia"},"content":{"rendered":"<p style=\"text-align: left;\"><ul id='GTTabs_ul_11363' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11363' class='GTTabs_curr'><a  id=\"11363_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11363' ><a  id=\"11363_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_11363'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<div id=\"attachment_11366\" style=\"width: 310px\" class=\"wp-caption alignright\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/terreno.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-11366\" data-attachment-id=\"11366\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11366\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/terreno.jpg\" data-orig-size=\"401,324\" 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=\"O Terreno da D.\u00aa Ant\u00f3nia\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/terreno.jpg\" class=\"  wp-image-11366\" title=\"O Terreno da D.\u00aa Ant\u00f3nia\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/terreno.jpg\" alt=\"\" width=\"300\" height=\"242\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/terreno.jpg 401w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/terreno-300x242.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/terreno-150x121.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/terreno-400x323.jpg 400w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><p id=\"caption-attachment-11366\" class=\"wp-caption-text\">O terreno da D.\u00aa Ant\u00f3nia<\/p><\/div>\n<p>A D.\u00aa Ant\u00f3nia dividiu o seu terreno em tr\u00eas parcelas quadradas, uma com $100$ m<sup>2<\/sup> de \u00e1rea, outra com $144$ m<sup>2<\/sup> e outra com $5$ m de comprimento do lado, como podes ver na figura.<\/p>\n<ol>\n<li>Quantos metros de rede deve comprar, se pretende ved\u00e1-lo ap\u00f3s ter colocado uma porta com $70$ cm de largura?<\/li>\n<li>Se cada metro de rede custar $12$ \u20ac, quanto ir\u00e1 gastar, no m\u00ednimo, para vedar o terreno? Escreve o pre\u00e7o por extenso.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11363' onClick='GTTabs_show(1,11363)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11363'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/terreno.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11366\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11366\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/terreno.jpg\" data-orig-size=\"401,324\" 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=\"O Terreno da D.\u00aa Ant\u00f3nia\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/terreno.jpg\" class=\"aligncenter wp-image-11366\" title=\"O Terreno da D.\u00aa Ant\u00f3nia\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/terreno.jpg\" alt=\"\" width=\"300\" height=\"242\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/terreno.jpg 401w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/terreno-300x242.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/terreno-150x121.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/terreno-400x323.jpg 400w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>\u00ad<\/p>\n<ol>\n<li>O lado da\u00a0parcela maior tem $\\sqrt {144}\u00a0 = 12$ m de comprimento e o da parcela interm\u00e9dia tem $\\sqrt {100}\u00a0 = 10$ m.\n<p>Comecemos por calcular o per\u00edmetro do terreno da D.\u00aa Ant\u00f3nia:<br \/>\n$$P = 3 \\times 5 + 3 \\times 10 + 4 \\times 12 &#8211; \\underbrace {\\left( {5 + 10} \\right)}_{{\\text{limites sobrepostos}}} = 15 + 30 + 48 &#8211; 15 = 78\\,m$$<br \/>\nComo a porta tem $70$ cm de largura, o comprimento da rede a comprar deve ser $0,7$ m inferior ao per\u00edmetro do terreno.<\/p>\n<p>Portanto, a D.\u00aa Ant\u00f3nia deve comprar $78 &#8211; 0,7 = 77,3$ m de rede.<br \/>\n\u00ad<\/p>\n<\/li>\n<li>No m\u00ednimo, a D.\u00aa Ant\u00f3nia ir\u00e1 gastar $77,3 \\times 12 = 627,60$ \u20ac (seiscentos e vinte e sete euros e sessenta c\u00eantimos) para vedar o seu terreno.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11363' onClick='GTTabs_show(0,11363)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A D.\u00aa Ant\u00f3nia dividiu o seu terreno em tr\u00eas parcelas quadradas, uma com $100$ m2 de \u00e1rea, outra com $144$ m2 e outra com $5$ m de comprimento do lado, como&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20736,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[317,97,318],"tags":[108,335,339],"series":[],"class_list":["post-11363","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-7-o-ano","category-aplicando","category-numeros-inteiros","tag-area","tag-perimetro","tag-raiz-quadrada"],"views":3319,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/7V1Pag038-5_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11363","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=11363"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11363\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20736"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11363"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11363"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11363"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11363"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}