{"id":14213,"date":"2018-03-31T00:22:40","date_gmt":"2018-03-30T23:22:40","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14213"},"modified":"2022-01-11T11:46:42","modified_gmt":"2022-01-11T11:46:42","slug":"o-perimetro-e-a-area-de-um-triangulo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14213","title":{"rendered":"O per\u00edmetro e a \u00e1rea de um tri\u00e2ngulo"},"content":{"rendered":"<p><ul id='GTTabs_ul_14213' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14213' class='GTTabs_curr'><a  id=\"14213_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14213' ><a  id=\"14213_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_14213'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag61-9.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14214\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14214\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag61-9.png\" data-orig-size=\"350,245\" 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=\"Tri\u00e2ngulo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag61-9.png\" class=\"alignright size-medium wp-image-14214\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag61-9-300x210.png\" alt=\"\" width=\"300\" height=\"210\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag61-9-300x210.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag61-9.png 350w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>No tri\u00e2ngulo ret\u00e2ngulo da figura, a hipotenusa mede mais 4 cm do que o cateto [<em>AB<\/em>] e\u00a0\\({\\mathop{\\rm sen}\\nolimits} \\widehat C = 0,6\\).<\/p>\n<p>Calcula o\u00a0per\u00edmetro e a \u00e1rea do tri\u00e2ngulo [<em>ABC<\/em>]<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14213' onClick='GTTabs_show(1,14213)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14213'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag61-9.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14214\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14214\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag61-9.png\" data-orig-size=\"350,245\" 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=\"Tri\u00e2ngulo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag61-9.png\" class=\"alignright size-medium wp-image-14214\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag61-9-300x210.png\" alt=\"\" width=\"300\" height=\"210\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag61-9-300x210.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag61-9.png 350w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Ora,<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{\\mathop{\\rm sen}\\nolimits} \\widehat C = 0,6}&amp; \\Leftrightarrow &amp;{\\frac{{\\overline {AB} }}{{\\overline {BC} }} = 0,6}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {AB} = 0,6 \\times \\overline {BC} }\\end{array}\\]<\/p>\n<p>Como\u00a0\\(\\overline {BC} = \\overline {AB} + 4\\), vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\overline {AB} = 0,6 \\times \\left( {\\overline {AB} + 4} \\right)}&amp; \\Leftrightarrow &amp;{0,4\\overline {AB} = 2,4}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {AB} = 6}\\end{array}\\]<\/p>\n<p>Aplicando o Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo [<em>ABC<\/em>], vem:<\/p>\n<p>\\[\\overline {AC} = \\sqrt {{{\\overline {BC} }^2} &#8211; {{\\overline {AB} }^2}} = \\sqrt {{{10}^2} &#8211; {6^2}} = 8\\]<\/p>\n<p>\u00ad<br \/>\nLogo, o per\u00edmetro, em cent\u00edmetros, e a \u00e1rea, em cent\u00edmetros quadrados, do tri\u00e2ngulo [<em>ABC<\/em>] s\u00e3o, respetivamente:<\/p>\n<p>\\[{P_{\\left[ {ABC} \\right]}} = \\overline {AB} + \\overline {AC} + \\overline {BC} = 6 + 8 + 10 = 24\\]<\/p>\n<p>\\[{A_{\\left[ {ABC} \\right]}} = \\frac{{\\overline {AB} \\times \\overline {AC} }}{2} = \\frac{{6 \\times 8}}{2} = 24\\]<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14213' onClick='GTTabs_show(0,14213)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado No tri\u00e2ngulo ret\u00e2ngulo da figura, a hipotenusa mede mais 4 cm do que o cateto [AB] e\u00a0\\({\\mathop{\\rm sen}\\nolimits} \\widehat C = 0,6\\). Calcula o\u00a0per\u00edmetro e a \u00e1rea do tri\u00e2ngulo [ABC] Resolu\u00e7\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14215,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,489],"tags":[426,491,490,492],"series":[],"class_list":["post-14213","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-trigonometria-9--ano","tag-9-o-ano","tag-cosseno","tag-seno","tag-tangente"],"views":2631,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag61-9a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14213","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=14213"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14213\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14215"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14213"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14213"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14213"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14213"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}