{"id":11373,"date":"2012-11-15T20:02:18","date_gmt":"2012-11-15T20:02:18","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11373"},"modified":"2022-01-20T14:15:06","modified_gmt":"2022-01-20T14:15:06","slug":"o-quintal-do-joao","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11373","title":{"rendered":"O quintal do Jo\u00e3o"},"content":{"rendered":"<p><ul id='GTTabs_ul_11373' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11373' class='GTTabs_curr'><a  id=\"11373_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11373' ><a  id=\"11373_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_11373'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/horta.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11377\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11377\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/horta.jpg\" data-orig-size=\"446,463\" 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=\"Quintal\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/horta.jpg\" class=\"alignright wp-image-11377\" title=\"Quintal\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/horta.jpg\" alt=\"\" width=\"320\" height=\"332\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/horta.jpg 446w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/horta-288x300.jpg 288w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/horta-144x150.jpg 144w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/horta-400x415.jpg 400w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/a>O Jo\u00e3o tem um terreno retangular onde h\u00e1 um galinheiro e uma coelheira tamb\u00e9m retangulares e uma horta quadrada, cujas medidas de \u00e1rea est\u00e3o indicadas na figura.<\/p>\n<p>O Jo\u00e3o cercou a horta, o galinheiro e a coelheira com cercas feitas com diferentes n\u00fameros de fios de arame, como indicado na figura.<\/p>\n<p>Quantos metros de arame ele usou?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11373' onClick='GTTabs_show(1,11373)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11373'>\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\/horta.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11377\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11377\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/horta.jpg\" data-orig-size=\"446,463\" 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=\"Quintal\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/horta.jpg\" class=\"alignright wp-image-11377\" title=\"Quintal\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/horta.jpg\" alt=\"\" width=\"320\" height=\"332\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/horta.jpg 446w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/horta-288x300.jpg 288w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/horta-144x150.jpg 144w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/horta-400x415.jpg 400w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/a>O comprimento do lado da horta \u00e9 ${l_H} = \\sqrt {100}\u00a0 = 10$ m.<\/p>\n<p>O galinheiro e a horta t\u00eam iguais comprimentos. Logo, o comprimento do galinheiro \u00e9 ${c_G} = 10$ m.<\/p>\n<p>Como a \u00e1rea de um ret\u00e2ngulo pode ser expressa por ${A_{\\operatorname{Re} t\u00e2ngulo}} = c \\times l$, ent\u00e3o a largura do galinheiro \u00e9 ${l_G} = \\frac{{50}}{{10}} = 5$ m.<\/p>\n<p>Assim, a coelheira tem ${c_C} = {l_H} + {l_G} = 10 + 5 = 15$ m de comprimento.<\/p>\n<p>E, por \u00faltimo, a coelheira tem ${l_C} = \\frac{{30}}{{15}} = 2$ m de largura.<\/p>\n<p>\u00ad<\/p>\n<p>Quantidade de arame usado na cerca da coelheira: $2 \\times \\left( {2 \\times 15 + 2 \\times 2} \\right) = 2 \\times 34 = 68$ m.<\/p>\n<p>Quantidade de arame gasto na cerca tripla da horta: $3 \\times \\left( {10 + 10} \\right) = 60$ m.<\/p>\n<p>Quantidade da arame gasto na cerca qu\u00e1drupla do galinheiro: $4 \\times \\left( {2 \\times 10 + 5} \\right) = 100$ m.<\/p>\n<\/p>\n<p>Portanto, o Jo\u00e3o usou $68 + 60 + 100 = 228$ m de rede nas suas cercas.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11373' onClick='GTTabs_show(0,11373)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O Jo\u00e3o tem um terreno retangular onde h\u00e1 um galinheiro e uma coelheira tamb\u00e9m retangulares e uma horta quadrada, cujas medidas de \u00e1rea est\u00e3o indicadas na figura. O Jo\u00e3o cercou a&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20738,"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-11373","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":5219,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/11\/7V1Pag039-7_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11373","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=11373"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11373\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20738"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11373"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11373"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11373"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11373"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}