{"id":6210,"date":"2010-11-28T00:17:36","date_gmt":"2010-11-28T00:17:36","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6210"},"modified":"2022-01-19T19:09:10","modified_gmt":"2022-01-19T19:09:10","slug":"no-rectangulo-ao-lado","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6210","title":{"rendered":"No ret\u00e2ngulo ao lado"},"content":{"rendered":"<p><ul id='GTTabs_ul_6210' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6210' class='GTTabs_curr'><a  id=\"6210_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6210' ><a  id=\"6210_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_6210'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag33-13.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6211\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6211\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag33-13.jpg\" data-orig-size=\"355,307\" 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=\"Rect\u00e2ngulo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag33-13.jpg\" class=\"alignright wp-image-6211\" title=\"Rect\u00e2ngulo\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag33-13-300x259.jpg\" alt=\"\" width=\"240\" height=\"208\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag33-13-300x259.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag33-13-150x129.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag33-13.jpg 355w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>No ret\u00e2ngulo ao lado, calcula $\\overline{AM}$.<\/p>\n<p>As medidas est\u00e3o indicadas numa mesma unidade.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6210' onClick='GTTabs_show(1,6210)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6210'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag33-13.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6211\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6211\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag33-13.jpg\" data-orig-size=\"355,307\" 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=\"Rect\u00e2ngulo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag33-13.jpg\" class=\"alignright wp-image-6211\" title=\"Rect\u00e2ngulo\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag33-13-300x259.jpg\" alt=\"\" width=\"240\" height=\"208\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag33-13-300x259.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag33-13-150x129.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag33-13.jpg 355w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>Aplicando o Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo [BCD], temos:<\/p>\n<p style=\"text-align: center;\">$\\begin{array}{*{35}{l}}<br \/>\n{{\\overline{BD}}^{2}}={{8}^{2}}+{{6}^{2}} &amp; \\Leftrightarrow\u00a0 &amp; {{\\overline{BD}}^{2}}=64+36\u00a0 \\\\<br \/>\n{} &amp; {} &amp; {{\\overline{BD}}^{2}}=100\u00a0 \\\\<br \/>\n{} &amp; {} &amp; \\overline{BD}=10\u00a0 \\\\<br \/>\n\\end{array}$<\/p>\n<p>Num tri\u00e2ngulo ret\u00e2ngulo, a altura relativa \u00e0 hipotenusa divide-o em dois tri\u00e2ngulos ret\u00e2ngulos semelhantes entre si e semelhantes ao tri\u00e2ngulo ret\u00e2ngulo inicial.<\/p>\n<p>Por isso, considerando os tri\u00e2ngulos [AMD] e [BCD], tem-se: $\\frac{\\overline{AM}}{\\overline{CD}}=\\frac{\\overline{AD}}{\\overline{BD}}$.<\/p>\n<p>Logo, vem:<\/p>\n<p>\\[\\frac{\\overline{AM}}{6}=\\frac{8}{10}\\Leftrightarrow \\overline{AM}=\\frac{6\\times 8}{10}\\Leftrightarrow \\overline{AM}=4,8\\]<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6210' onClick='GTTabs_show(0,6210)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado No ret\u00e2ngulo ao lado, calcula $\\overline{AM}$. As medidas est\u00e3o indicadas numa mesma unidade. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20676,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,112],"tags":[424,67,118],"series":[],"class_list":["post-6210","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-geometria","tag-teorema-de-pitagoras"],"views":1459,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/8V1Pag033-13_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6210","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=6210"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6210\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20676"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6210"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6210"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6210"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6210"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}