{"id":3424,"date":"2010-10-03T17:08:25","date_gmt":"2010-10-03T16:08:25","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=3424"},"modified":"2022-01-18T22:32:23","modified_gmt":"2022-01-18T22:32:23","slug":"a-area-do-triangulo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=3424","title":{"rendered":"A \u00e1rea do tri\u00e2ngulo"},"content":{"rendered":"<p><ul id='GTTabs_ul_3424' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_3424' class='GTTabs_curr'><a  id=\"3424_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_3424' ><a  id=\"3424_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_3424'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/triangulo.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"3425\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=3425\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/triangulo.jpg\" data-orig-size=\"389,303\" 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=\"O tri\u00e2ngulo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/triangulo.jpg\" class=\"alignright wp-image-3425\" title=\"O tri\u00e2ngulo\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/triangulo.jpg\" alt=\"\" width=\"300\" height=\"234\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/triangulo.jpg 389w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/triangulo-300x233.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/triangulo-150x116.jpg 150w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>A \u00e1rea do tri\u00e2ngulo \u00e9 9 cm<sup>2<\/sup>.<\/p>\n<p>Qual \u00e9 o seu per\u00edmetro?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_3424' onClick='GTTabs_show(1,3424)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_3424'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"3425\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=3425\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/triangulo.jpg\" data-orig-size=\"389,303\" 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=\"O tri\u00e2ngulo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/triangulo.jpg\" class=\"alignright wp-image-3425\" title=\"O tri\u00e2ngulo\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/triangulo.jpg\" alt=\"\" width=\"300\" height=\"234\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/triangulo.jpg 389w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/triangulo-300x233.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/triangulo-150x116.jpg 150w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/>Sabendo que a \u00e1rea de um tri\u00e2ngulo pode ser expressa por\u00a0\\[{{A}_{Tri\\hat{a}ngulo}}=\\frac{b\\times h}{2}\\] onde <em>b<\/em> e <em>h<\/em> designam, respetivamente, os comprimentos da base e da altura (estes segmentos t\u00eam de ser perpendiculares), temos: \\[\\frac{4\\times (x+2)}{2}=9\\ \\ \\ (\\text{Porqu }\\!\\!\\hat{\\mathrm{e}}\\!\\!\\text{ ?})\\]<\/p>\n<p>Resolvendo a equa\u00e7\u00e3o, vem: \\[\\begin{array}{*{35}{l}}<br \/>\n\\frac{4\\times (x+2)}{2}=9 &amp; \\Leftrightarrow\u00a0 &amp; \\frac{1}{2}\\times 4\\times (x+2)=9\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 2\\times (x+2)=9\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 2x+4=9\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 2x=5\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x=\\frac{5}{2}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x=2,5\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>Portanto:<\/p>\n<ul>\n<li>a base do tri\u00e2ngulo tem de comprimento: $2,5+2=4,5$ (cm);<\/li>\n<li>o maior dos lados tem de comprimento: $2\\times 2,5+1=6$ (cm);<\/li>\n<li>o menor dos lados tem de comprimento: $2,5$ (cm).<\/li>\n<\/ul>\n<p>O\u00a0tri\u00e2ngulo tem ${{P}_{T}}=4,5+6+2,5=13$ cent\u00edmetros de per\u00edmetro.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_3424' onClick='GTTabs_show(0,3424)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A \u00e1rea do tri\u00e2ngulo \u00e9 9 cm2. Qual \u00e9 o seu per\u00edmetro? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20612,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,101],"tags":[424,425],"series":[],"class_list":["post-3424","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes","tag-8-o-ano","tag-equacoes"],"views":1968,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/7V2Pag067-13_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3424","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=3424"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3424\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20612"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3424"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3424"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3424"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=3424"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}