{"id":12875,"date":"2017-10-30T01:58:56","date_gmt":"2017-10-30T01:58:56","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=12875"},"modified":"2022-01-15T23:49:23","modified_gmt":"2022-01-15T23:49:23","slug":"um-terreno-tem-a-forma-de-um-triangulo-isosceles","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=12875","title":{"rendered":"Um terreno tem a forma de um tri\u00e2ngulo is\u00f3sceles"},"content":{"rendered":"<p><ul id='GTTabs_ul_12875' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_12875' class='GTTabs_curr'><a  id=\"12875_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_12875' ><a  id=\"12875_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_12875'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/TrianguloIsosceles.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"12876\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=12876\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/TrianguloIsosceles.png\" data-orig-size=\"398,288\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Tri\u00e2ngulo Is\u00f3sceles\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/TrianguloIsosceles.png\" class=\"alignright wp-image-12876\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/TrianguloIsosceles-300x217.png\" alt=\"\" width=\"240\" height=\"174\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/TrianguloIsosceles-300x217.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/TrianguloIsosceles.png 398w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>Um terreno tem a forma de um tri\u00e2ngulo is\u00f3sceles [ABC], tal que\u00a0\\(\\overline {AB} = \\overline {AC} \\) e P \u00e9 um ponto do lado [AB] tal que\u00a0\\(\\overline {PB} = 100\\) m e\u00a0\\(\\overline {AP} = \\overline {BC} \\).<\/p>\n<p>Foram feitas duas medi\u00e7\u00f5es aproximadas, respetivamente por defeito e por excesso, ao per\u00edmetro do terreno, tendo-se obtido os seguintes resultados: 821 metros e 827 metros.<\/p>\n<p>Determina dois intervalos de amplitude inferior ou igual a 2, tais que a medida do comprimento, em metros, dos lados [AB] e [BC], perten\u00e7am respetivamente a esses intervalos.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_12875' onClick='GTTabs_show(1,12875)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_12875'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>De acordo com os dados, tem-se:\u00a0\\({P_{\\left[ {ABC} \\right]}} = 2 \\times \\overline {AB} + \\overline {BC} = 2 \\times \\left( {\\overline {BC} + 100} \\right) + \\overline {BC} = 3 \\times \\overline {BC} + 200\\).<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/TrianguloIsosceles.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"12876\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=12876\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/TrianguloIsosceles.png\" data-orig-size=\"398,288\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Tri\u00e2ngulo Is\u00f3sceles\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/TrianguloIsosceles.png\" class=\"alignright wp-image-12876\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/TrianguloIsosceles-300x217.png\" alt=\"\" width=\"240\" height=\"174\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/TrianguloIsosceles-300x217.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/TrianguloIsosceles.png 398w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>Assim, vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{821 &lt; {P_{\\left[ {ABC} \\right]}} &lt; 827}&amp; \\Leftrightarrow &amp;{821 &lt; 3 \\times \\overline {BC} + 200 &lt; 827}\\\\{}&amp; \\Leftrightarrow &amp;{621 &lt; 3 \\times \\overline {BC} &lt; 627}\\\\{}&amp; \\Leftrightarrow &amp;{207 &lt; \\overline {BC} &lt; 209}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {BC} \\in \\left] {207,\\;209} \\right[}\\end{array}\\]<\/p>\n<p>Por \u00faltimo, temos:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{207 &lt; \\overline {BC} &lt; 209}&amp; \\Leftrightarrow &amp;{207 + 100 &lt; \\overline {BC} + 100 &lt; 209 + 100}\\\\{}&amp; \\Leftrightarrow &amp;{307 &lt; \\overline {AB} &lt; 309}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {AB} \\in \\left] {307,\\;309} \\right[}\\end{array}\\]<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_12875' onClick='GTTabs_show(0,12875)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um terreno tem a forma de um tri\u00e2ngulo is\u00f3sceles [ABC], tal que\u00a0\\(\\overline {AB} = \\overline {AC} \\) e P \u00e9 um ponto do lado [AB] tal que\u00a0\\(\\overline {PB} = 100\\) m&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20315,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,258],"tags":[443,442],"series":[],"class_list":["post-12875","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-os-numeros-reais","tag-enquadramento","tag-valor-aproximado"],"views":2910,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/9V1Pag031-8_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12875","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=12875"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12875\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20315"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12875"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12875"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12875"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=12875"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}