{"id":6888,"date":"2011-05-25T00:06:27","date_gmt":"2011-05-24T23:06:27","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6888"},"modified":"2022-01-18T19:14:33","modified_gmt":"2022-01-18T19:14:33","slug":"um-triangulo-rectangulo-4","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6888","title":{"rendered":"Um tri\u00e2ngulo ret\u00e2ngulo"},"content":{"rendered":"<p><ul id='GTTabs_ul_6888' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6888' class='GTTabs_curr'><a  id=\"6888_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6888' ><a  id=\"6888_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_6888'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Determina o valor de x de modo que o tri\u00e2ngulo seja ret\u00e2ngulo.<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/2v8pag81-6.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6889\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6889\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/2v8pag81-6.jpg\" data-orig-size=\"388,322\" 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=\"Tri\u00e2ngulo rect\u00e2ngulo\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/2v8pag81-6-300x248.jpg\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/2v8pag81-6.jpg\" class=\"aligncenter wp-image-6889\" title=\"Tri\u00e2ngulo rect\u00e2ngulo\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/2v8pag81-6.jpg\" alt=\"\" width=\"240\" height=\"199\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/2v8pag81-6.jpg 388w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/2v8pag81-6-300x248.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/2v8pag81-6-150x124.jpg 150w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6888' onClick='GTTabs_show(1,6888)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6888'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/2v8pag81-6.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6889\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6889\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/2v8pag81-6.jpg\" data-orig-size=\"388,322\" 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=\"Tri\u00e2ngulo rect\u00e2ngulo\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/2v8pag81-6-300x248.jpg\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/2v8pag81-6.jpg\" class=\"alignright wp-image-6889\" title=\"Tri\u00e2ngulo rect\u00e2ngulo\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/2v8pag81-6.jpg\" alt=\"\" width=\"240\" height=\"199\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/2v8pag81-6.jpg 388w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/2v8pag81-6-300x248.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/2v8pag81-6-150x124.jpg 150w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>Para que o tri\u00e2ngulo seja ret\u00e2ngulo ter\u00e1 de se verificar: ${{x}^{2}}+{{9}^{2}}={{(x+4)}^{2}}$. (Porqu\u00ea?)<\/p>\n<p>Assim, temos:<\/p>\n<p>\\[\\begin{array}{*{35}{l}}<br \/>\n{{x}^{2}}+{{9}^{2}}={{(x+4)}^{2}} &amp; \\Leftrightarrow\u00a0 &amp; {{x}^{2}}+81=(x+4)(x+4)\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; {{x}^{2}}+81={{x}^{2}}+4x+4x+16\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 8x=65\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x=\\frac{65}{8}\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6888' onClick='GTTabs_show(0,6888)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Determina o valor de x de modo que o tri\u00e2ngulo seja ret\u00e2ngulo. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20599,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,193],"tags":[195],"series":[],"class_list":["post-6888","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-de-grau-superior-ao-1-","tag-operacoes-com-polinomios"],"views":2464,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/05\/8V2Pag081-6_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6888","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=6888"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6888\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20599"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6888"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6888"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6888"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6888"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}