{"id":14513,"date":"2018-04-14T22:36:19","date_gmt":"2018-04-14T21:36:19","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14513"},"modified":"2022-01-07T22:11:13","modified_gmt":"2022-01-07T22:11:13","slug":"uma-calcada","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14513","title":{"rendered":"Uma cal\u00e7ada"},"content":{"rendered":"<p><ul id='GTTabs_ul_14513' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14513' class='GTTabs_curr'><a  id=\"14513_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14513' ><a  id=\"14513_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_14513'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-19.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14514\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14514\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-19.png\" data-orig-size=\"336,394\" 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=\"Cal\u00e7ada\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-19.png\" class=\"alignright size-medium wp-image-14514\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-19-256x300.png\" alt=\"\" width=\"256\" height=\"300\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-19-256x300.png 256w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-19.png 336w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/a>O Sr. Jos\u00e9 foi contratado para fazer uma cal\u00e7ada \u00e0 volta de dois lados de um terreno retangular. O terreno mede 20 metros por 30 metros, como indica a figura, e a cal\u00e7ada deve ter sempre a mesma largura.<\/p>\n<p>Sabendo que o Sr. Jos\u00e9 disp\u00f5e de 72 m<sup>2<\/sup> de lajetas de pavimento para fazer a obra, qual dever\u00e1 ser a largura, arredondada \u00e0s d\u00e9cimas, da cal\u00e7ada?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14513' onClick='GTTabs_show(1,14513)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14513'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-19.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14514\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14514\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-19.png\" data-orig-size=\"336,394\" 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=\"Cal\u00e7ada\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-19.png\" class=\"alignright size-medium wp-image-14514\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-19-256x300.png\" alt=\"\" width=\"256\" height=\"300\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-19-256x300.png 256w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-19.png 336w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/a>Seja <em>x<\/em>, em metros, a largura da cal\u00e7ada.<\/p>\n<p>Decompondo a cal\u00e7ada em dois ret\u00e2ngulos e um quadrado, uma express\u00e3o da sua \u00e1rea, em fun\u00e7\u00e3o de <em>x<\/em>, \u00e9:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{A_C}}&amp; = &amp;{30 \\times x + x \\times x + 20 \\times x}\\\\{}&amp; = &amp;{30x + {x^2} + 20x}\\\\{}&amp; = &amp;{{x^2} + 50x}\\end{array}\\]<\/p>\n<p>Considerando valor m\u00e1ximo poss\u00edvel para a \u00e1rea da cal\u00e7ada, temos:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{A_C} = 72}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{{x^2} + 50x = 72}&amp; \\wedge &amp;{x &gt; 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{{x^2} + 50x &#8211; 72 = 0}&amp; \\wedge &amp;{x &gt; 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = \\frac{{ &#8211; 50 \\mp \\sqrt {2500 + 288} }}{2}}&amp; \\wedge &amp;{x &gt; 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = \\frac{{ &#8211; 50 \\mp 2\\sqrt {697} }}{2}}&amp; \\wedge &amp;{x &gt; 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{\\left( {\\begin{array}{*{20}{c}}{x = &#8211; 25 &#8211; \\sqrt {697} }&amp; \\vee &amp;{x = &#8211; 25 + \\sqrt {697} }\\end{array}} \\right)}&amp; \\wedge &amp;{x &gt; 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{x = &#8211; 25 + \\sqrt {697} }\\\\{}&amp;{}&amp;{x \\approx 1,4}\\end{array}\\]<\/p>\n<p>A largura da cal\u00e7ada deve ser, aproximadamente, 1,4 metros.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14513' onClick='GTTabs_show(0,14513)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O Sr. Jos\u00e9 foi contratado para fazer uma cal\u00e7ada \u00e0 volta de dois lados de um terreno retangular. O terreno mede 20 metros por 30 metros, como indica a figura, e&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14516,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,303],"tags":[426,108,306,304],"series":[],"class_list":["post-14513","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-equacoes-do-2-o-grau","tag-9-o-ano","tag-area","tag-equacao-do-2-o-grau","tag-formula-resolvente"],"views":2444,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-19a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14513","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=14513"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14513\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14516"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14513"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14513"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14513"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14513"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}