{"id":4100,"date":"2023-11-30T18:09:56","date_gmt":"2023-11-30T21:09:56","guid":{"rendered":"https:\/\/xequematenem.com.br\/blog\/?p=4100"},"modified":"2024-03-06T08:34:55","modified_gmt":"2024-03-06T11:34:55","slug":"questao-179-enem-2013","status":"publish","type":"post","link":"https:\/\/xequematenem.com.br\/blog\/questao-179-enem-2013\/","title":{"rendered":"Quest\u00e3o 179 &#8211; ENEM 2013"},"content":{"rendered":"\n<p class=\"has-text-align-center wp-block-paragraph\">Quest\u00e3o 179 &#8211; Trigonometria<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">O dono de um s\u00edtio pretende colocar uma haste de sustenta\u00e7\u00e3o para melhor firmar dois postes de <strong>comprimentos iguais a 6 m e 4 m.<\/strong> A figura representa a situa\u00e7\u00e3o real na qual os postes s\u00e3o descritos pelos <strong>segmentos AC e BD e a haste \u00e9 representada pelo segmento EF, <\/strong>todos perpendiculares ao solo, que \u00e9 indicado pelo segmento de reta AB. <strong>Os segmentos AD e BC representam cabos de a\u00e7o que ser\u00e3o instalados.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"329\" height=\"120\" data-src=\"https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2023\/11\/image-16.png\" alt=\"\" class=\"wp-image-4101 lazyload\" title=\"\" data-srcset=\"https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2023\/11\/image-16.png 329w, https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2023\/11\/image-16-300x109.png 300w\" data-sizes=\"(max-width: 329px) 100vw, 329px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 329px; --smush-placeholder-aspect-ratio: 329\/120;\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Qual deve ser o valor do comprimento da haste EF?<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A) 1 m<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B) 2 m<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C) 2,4 m<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D) 3 m<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">E) 2\u221a6 m<\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size wp-block-paragraph\"><strong>Solu\u00e7\u00e3o<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Podemos observar que temos um tri\u00e2ngulo ret\u00e2ngulo ABC e um EFB que tem a rela\u00e7\u00e3o de semelhan\u00e7a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img fetchpriority=\"high\" decoding=\"async\" width=\"970\" height=\"508\" src=\"https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2023\/11\/image-1.jpeg\" alt=\"\" class=\"wp-image-4102\" title=\"\" srcset=\"https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2023\/11\/image-1.jpeg 970w, https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2023\/11\/image-1-300x157.jpeg 300w, https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2023\/11\/image-1-768x402.jpeg 768w\" sizes=\"(max-width: 970px) 100vw, 970px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Podemos dizer que<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">4\/(z+y) = x\/y<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Multiplicando cruzado temos que<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;x(x+y) = 4y<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Tamb\u00e9m temos a rela\u00e7\u00e3o de semelhan\u00e7a entre os tri\u00e2ngulos ABD e AEF, onde:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"992\" height=\"498\" data-src=\"https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2023\/11\/image-2.jpeg\" alt=\"\" class=\"wp-image-4103 lazyload\" title=\"\" data-srcset=\"https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2023\/11\/image-2.jpeg 992w, https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2023\/11\/image-2-300x151.jpeg 300w, https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2023\/11\/image-2-768x386.jpeg 768w\" data-sizes=\"(max-width: 992px) 100vw, 992px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 992px; --smush-placeholder-aspect-ratio: 992\/498;\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">6\/(z+y) = x\/z<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Multiplicando cruzado temos que<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">x(z+y) = 6z<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">J\u00e1 que&nbsp; x(x+y) = 4y e x(z+y) = 6z, podemos concluir que<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">4y = 6z, ou seja<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">z = 4y\/6 = 2y\/3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substituindo na primeira equa\u00e7\u00e3o, temos a seguinte igualdade<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">x(2y\/3 + y) = 4y<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">x(5y\/3) = 4y<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">x = 4y.(3\/5y)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">x = 12\/5 = 2,4 m<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Alternativa C<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Quest\u00e3o 179 &#8211; Trigonometria O dono de um s\u00edtio pretende colocar uma haste de sustenta\u00e7\u00e3o para melhor firmar dois postes de comprimentos iguais a 6 m e 4 m. A figura representa a situa\u00e7\u00e3o real na qual os postes s\u00e3o descritos pelos segmentos AC e BD e a haste \u00e9 representada pelo segmento EF, todos [&hellip;]<\/p>\n","protected":false},"author":11,"featured_media":4101,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[17,26],"tags":[],"area-do-conhecimento":[132,118],"assunto":[32],"class_list":["post-4100","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-questoes-do-enem","category-26","area-do-conhecimento-matematica","area-do-conhecimento-matematica-e-suas-tecnologias","assunto-trigonometria"],"_links":{"self":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/posts\/4100","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/comments?post=4100"}],"version-history":[{"count":0,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/posts\/4100\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/media\/4101"}],"wp:attachment":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/media?parent=4100"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/categories?post=4100"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/tags?post=4100"},{"taxonomy":"area-do-conhecimento","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/area-do-conhecimento?post=4100"},{"taxonomy":"assunto","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/assunto?post=4100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}