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{"id":5689,"date":"2010-11-19T01:43:43","date_gmt":"2010-11-19T01:43:43","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=5689"},"modified":"2022-01-19T17:57:36","modified_gmt":"2022-01-19T17:57:36","slug":"um-telhado-de-quatro-aguas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=5689","title":{"rendered":"Um telhado de quatro \u00e1guas"},"content":{"rendered":"<p><ul id='GTTabs_ul_5689' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_5689' class='GTTabs_curr'><a  id=\"5689_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_5689' ><a  id=\"5689_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_5689'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>H\u00e1 casas constru\u00eddas com telhados de duas \u00e1guas e outras com telhados de quatro \u00e1guas.<\/p>\n<p>Na figura est\u00e1 representado um telhado com quatro \u00e1guas. Os n\u00fameros indicam as medidas em metros.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag24-7.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"5692\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=5692\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag24-7.jpg\" data-orig-size=\"775,333\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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=\"Telhado\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag24-7.jpg\" class=\"aligncenter wp-image-5692\" title=\"Telhado\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag24-7.jpg\" alt=\"\" width=\"540\" height=\"232\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag24-7.jpg 775w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag24-7-300x128.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag24-7-150x64.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag24-7-400x171.jpg 400w\" sizes=\"auto, (max-width: 540px) 100vw, 540px\" \/><\/a><br class=\"spacer_\" \/>\u00a0Sabendo que para cobrir 1 m<sup>2<\/sup> desse telhado s\u00e3o necess\u00e1rias 15 telhas:<\/p>\n<ol>\n<li>quantas telhas, no m\u00ednimo, ser\u00e3o utilizadas para cobrir esse telhado, se na cobertura houver uma perda de 3%?<\/li>\n<li>se dez telhas custam 5 \u20ac, quanto custar\u00e1 esse telhado?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_5689' onClick='GTTabs_show(1,5689)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_5689'>\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\/2010\/11\/pag24-7.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"5692\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=5692\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag24-7.jpg\" data-orig-size=\"775,333\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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=\"Telhado\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag24-7.jpg\" class=\"aligncenter wp-image-5692\" title=\"Telhado\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag24-7.jpg\" alt=\"\" width=\"540\" height=\"232\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag24-7.jpg 775w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag24-7-300x128.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag24-7-150x64.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag24-7-400x171.jpg 400w\" sizes=\"auto, (max-width: 540px) 100vw, 540px\" \/><\/a><\/p>\n<\/p>\n<ol>\n<li>Comecemos por determinar a \u00e1rea do telhado: \\[\\begin{array}{*{35}{l}}<br \/>\n{{A}_{Telhado}} &amp; = &amp; 2\\times {{A}_{Tri\\hat{a}ngulo}}+2\\times {{A}_{Trap\\acute{e}zio}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 2\\times \\left( \\frac{6,75\\times 5,6}{2} \\right)+2\\times \\left( \\frac{18+8}{2}\\times 4 \\right)\u00a0 \\\\<br \/>\n{} &amp; = &amp; 6,75\\times 5,6+26\\times 4\u00a0 \\\\<br \/>\n{} &amp; = &amp; 37,8+104\u00a0 \\\\<br \/>\n{} &amp; = &amp; 141,8\\,\\,{{m}^{2}}\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>Se para cobrir 1 m<sup>2<\/sup> desse telhado s\u00e3o necess\u00e1rias 15 telhas, ent\u00e3o seriam necess\u00e1rias $141,8\\times 15=2127$ telhas para efetuar a cobertura. Mas, como h\u00e1 uma perda de 3%, esse valor ser\u00e1 acrescido de $2127\\times 0,03\\simeq 64$ telhas.<\/p>\n<p>Logo, ser\u00e3o necess\u00e1rias 2191 telhas, no m\u00ednimo.<br \/>\n\u00ad<\/p>\n<\/li>\n<li>\n<p>Se dez telhas custam 5 \u20ac, ent\u00e3o\u00a0esse telhado custar\u00e1 $\\frac{2191}{10}\\times 5=1095,50$ \u20ac.<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_5689' onClick='GTTabs_show(0,5689)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado H\u00e1 casas constru\u00eddas com telhados de duas \u00e1guas e outras com telhados de quatro \u00e1guas. Na figura est\u00e1 representado um telhado com quatro \u00e1guas. Os n\u00fameros indicam as medidas em metros.&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20658,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,112],"tags":[424,108,67,113,106],"series":[],"class_list":["post-5689","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-decomposicao-de-figuras-teorema-de-pitagoras","tag-8-o-ano","tag-area","tag-geometria","tag-trapezio","tag-triangulos"],"views":27841,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/8V1Pag024-7_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/5689","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=5689"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/5689\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20658"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5689"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5689"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5689"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=5689"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}