{"id":10159,"date":"2012-10-06T01:51:47","date_gmt":"2012-10-06T00:51:47","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=10159"},"modified":"2021-12-26T19:28:27","modified_gmt":"2021-12-26T19:28:27","slug":"dois-triangulos-semelhantes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=10159","title":{"rendered":"Dois tri\u00e2ngulos semelhantes"},"content":{"rendered":"<p><ul id='GTTabs_ul_10159' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_10159' class='GTTabs_curr'><a  id=\"10159_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_10159' ><a  id=\"10159_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_10159'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Determine a medida da hipotenusa de um tri\u00e2ngulo ret\u00e2ngulo de per\u00edmetro igual a $24$ cm que \u00e9 semelhante a outro cujos catetos medem $3$ cm e $4$ cm.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_10159' onClick='GTTabs_show(1,10159)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_10159'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>De acordo com o Teorema de Pit\u00e1goras, a hipotenusa do tri\u00e2ngulo ret\u00e2ngulo cujas medidas dos catetos s\u00e3o conhecidas tem $5$ cm de comprimento.<\/p>\n<p>Assim, o per\u00edmetro deste tri\u00e2ngulo \u00e9 $P = 3 + 4 + 5 = 12$ cm.<\/p>\n<p>Como $r = \\frac{{P&#8217;}}{P} = \\frac{{24}}{{12}} = 2$, o primeiro dos tri\u00e2ngulos \u00e9 uma amplia\u00e7\u00e3o, com raz\u00e3o $2$, do tri\u00e2ngulo de catetos conhecidos.<\/p>\n<p>Logo, a hipotenusa do primeiro dos tri\u00e2ngulos tem $2 \\times 5 = 10$ cm de comprimento, pois as hipotenusas s\u00e3o lados correspondentes desses tri\u00e2ngulos.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_10159' onClick='GTTabs_show(0,10159)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Determine a medida da hipotenusa de um tri\u00e2ngulo ret\u00e2ngulo de per\u00edmetro igual a $24$ cm que \u00e9 semelhante a outro cujos catetos medem $3$ cm e $4$ cm. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19358,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[321,97,322],"tags":[429,67,430,149],"series":[],"class_list":["post-10159","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-10-o-ano","category-aplicando","category-modulo-inicial","tag-10-o-ano","tag-geometria","tag-modulo-inicial","tag-semelhanca-de-triangulos"],"views":2596,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/Dois_Triangulos_Semelhantes.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10159","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=10159"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/10159\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19358"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10159"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10159"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10159"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=10159"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}