{"id":8618,"date":"2012-04-19T23:37:13","date_gmt":"2012-04-19T22:37:13","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=8618"},"modified":"2022-01-16T11:42:32","modified_gmt":"2022-01-16T11:42:32","slug":"a-largura-da-calcada","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=8618","title":{"rendered":"A largura da cal\u00e7ada"},"content":{"rendered":"<p><ul id='GTTabs_ul_8618' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_8618' class='GTTabs_curr'><a  id=\"8618_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_8618' ><a  id=\"8618_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_8618'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-10.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"8619\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=8619\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-10.jpg\" data-orig-size=\"274,320\" 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=\"Cal\u00e7ada\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-10.jpg\" class=\"alignright wp-image-8619\" title=\"Cal\u00e7ada\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-10.jpg\" alt=\"\" width=\"240\" height=\"280\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-10.jpg 274w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-10-256x300.jpg 256w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-10-128x150.jpg 128w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>O Sr. Jos\u00e9 foi contratado para fazer uma cal\u00e7ada \u00e0 volta de dois lados de um terreno retangular.<\/p>\n<p>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 cal\u00e7ada, que pretende gastar na totalidade, qual dever\u00e1 ser a largura da cal\u00e7ada?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8618' onClick='GTTabs_show(1,8618)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_8618'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"8621\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=8621\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-10a.png\" data-orig-size=\"333,388\" 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;}\" data-image-title=\"Cal\u00e7ada\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-10a.png\" class=\"alignright wp-image-8621\" title=\"Cal\u00e7ada\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-10a.png\" alt=\"\" width=\"240\" height=\"280\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-10a.png 333w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-10a-257x300.png 257w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-10a-128x150.png 128w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/>Seja $x$, em metros, a largura da cal\u00e7ada.<\/p>\n<p>De acordo com a decomposi\u00e7\u00e3o apresentada, temos: $$\\begin{array}{*{20}{c}}<br \/>\n{{A_1}:}&amp;{30x} \\\\<br \/>\n{{A_2}:}&amp;{{x^2}} \\\\<br \/>\n{{A_3}:}&amp;{20x}<br \/>\n\\end{array}$$<\/p>\n<p>Assim, temos:<\/p>\n<p>$$\\begin{array}{*{20}{l}}<br \/>\n{30x + {x^2} + 20x = 72}&amp; \\Leftrightarrow &amp;{{x^2} + 50x &#8211; 72 = 0} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{x = \\frac{{ &#8211; 50 \\pm \\sqrt {2500 + 288} }}{2}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{x = \\frac{{ &#8211; 50 \\pm \\sqrt {2788} }}{2}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}<br \/>\n{x = \\frac{{ &#8211; 50 &#8211; \\sqrt {2788} }}{2}}&amp; \\vee &amp;{x = \\frac{{ &#8211; 50 + \\sqrt {2788} }}{2}}<br \/>\n\\end{array}}<br \/>\n\\end{array}$$<\/p>\n<p>Ora, $$\\begin{array}{*{20}{c}}<br \/>\n{{x_1} = \\frac{{ &#8211; 50 &#8211; \\sqrt {2788} }}{2} \\approx\u00a0 &#8211; 51,4}&amp;{\\text{e}}&amp;{{x_2} = \\frac{{ &#8211; 50 + \\sqrt {2788} }}{2} \\approx 1,4}<br \/>\n\\end{array}$$<\/p>\n<p>Portanto, a cal\u00e7ada deve ter 1,4 metros de largura.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8618' onClick='GTTabs_show(0,8618)'>&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":20354,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,303],"tags":[426,306],"series":[],"class_list":["post-8618","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-equacao-do-2-o-grau"],"views":3334,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9V2Pag069-10_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8618","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=8618"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8618\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20354"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8618"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8618"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8618"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=8618"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}