{"id":6684,"date":"2011-04-04T19:16:05","date_gmt":"2011-04-04T18:16:05","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6684"},"modified":"2022-01-05T22:31:36","modified_gmt":"2022-01-05T22:31:36","slug":"os-triangulos-lua-e-mir","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6684","title":{"rendered":"Os tri\u00e2ngulos [LUA] e [MIR]"},"content":{"rendered":"<p><ul id='GTTabs_ul_6684' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6684' class='GTTabs_curr'><a  id=\"6684_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6684' ><a  id=\"6684_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_6684'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Os tri\u00e2ngulos [LUA] e [MIR], que t\u00eam de comprimento dos lados, respetivamente, 15 cm, 18 cm, 21 cm e 20 cm, 24 cm, 30 cm, n\u00e3o s\u00e3o semelhantes. Porqu\u00ea?<\/p>\n<p>Que altera\u00e7\u00f5es poder\u00edamos fazer de modo que o segundo tri\u00e2ngulo fosse semelhante ao primeiro?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6684' onClick='GTTabs_show(1,6684)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6684'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<table class=\"aligncenter\" style=\"width: 80%;\" border=\"2\" cellspacing=\"4\" cellpadding=\"4\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" colspan=\"3\">Tri\u00e2ngulo [LUA]<\/td>\n<td><\/td>\n<td style=\"text-align: center;\" colspan=\"3\">Tri\u00e2ngulo [MIR]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">15 cm<\/td>\n<td style=\"text-align: center;\">18 cm<\/td>\n<td>21 cm<\/td>\n<td style=\"background-color: #96dbe0;\"><\/td>\n<td style=\"text-align: center;\">20 cm<\/td>\n<td style=\"text-align: center;\">24 cm<\/td>\n<td style=\"text-align: center;\">30 cm<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Os tri\u00e2ngulos n\u00e3o s\u00e3o semelhantes, pois os comprimentos dos lados correspondentes n\u00e3o s\u00e3o diretamente proporcionais:<\/p>\n<p>\\[\\begin{matrix} \u00a0\u00a0 \\frac{20}{15}=\\frac{24}{18}=0,75 &amp; e &amp; \\frac{21}{30}=0,7\u00a0 \\\\ \\end{matrix}\\]<\/p>\n<p>Para que o segundo tri\u00e2ngulo seja semelhante ao primeiro, basta alterar o comprimento do lado maior do tri\u00e2ngulo [MIR]:<\/p>\n<p>\\[\\frac{21}{x}=0,75\\Leftrightarrow x=\\frac{21}{0,75}\\Leftrightarrow x=28\\]<\/p>\n<p>Portanto, o segundo tri\u00e2ngulo \u00e9 semelhante ao primeiro se os seus lados tiverem de comprimento 20 cm, 24 cm e 28 cm.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6684' onClick='GTTabs_show(0,6684)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Os tri\u00e2ngulos [LUA] e [MIR], que t\u00eam de comprimento dos lados, respetivamente, 15 cm, 18 cm, 21 cm e 20 cm, 24 cm, 30 cm, n\u00e3o s\u00e3o semelhantes. Porqu\u00ea? Que altera\u00e7\u00f5es&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14083,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,151],"tags":[149],"series":[],"class_list":["post-6684","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-semelhanca-de-triangulos-8--ano","tag-semelhanca-de-triangulos"],"views":3221,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat28.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6684","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=6684"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6684\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14083"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6684"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6684"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6684"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6684"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}