\nEnunciado<\/b><\/span><\/p>\n
Observa a figura.<\/p>\n
$\"\"$ <\/a><\/p>\n
\n
Exprime, em fun\u00e7\u00e3o de x<\/em>, a \u00e1rea do ret\u00e2ngulo e do tri\u00e2ngulo da figura.<\/li>\n
Determina o valor de x<\/em> para o qual o tri\u00e2ngulo e o ret\u00e2ngulo tenham a mesma \u00e1rea.<\/li>\n<\/ol>\n
Resolu\u00e7\u00e3o >><\/a><\/span><\/div><\/div>\n\n
\nResolu\u00e7\u00e3o<\/b><\/span><\/p>\n
\n
Observa a figura.<\/p>\n<\/blockquote>\n
$\"\"$ <\/a><\/p>\n
\n
\n
Exprime, em fun\u00e7\u00e3o de x, a \u00e1rea do ret\u00e2ngulo e do tri\u00e2ngulo da figura.<\/blockquote>\n<\/li>\n
\n
Determina o valor de\u00a0x para o qual o tri\u00e2ngulo e o ret\u00e2ngulo tenham a mesma \u00e1rea.<\/blockquote>\n<\/li>\n<\/ol>\n
\u00a0<\/p>\n
\n
A \u00e1rea do ret\u00e2ngulo e do tri\u00e2ngulo podem ser expressas por: \${A_R} = \\left( {x + x} \\right)x = 2{x^2}\$ e \${A_T} = \\frac{{10 \\times x}}{2} = 5x\$.

<\/li>\n
Equacionando o problema e resolvendo a equa\u00e7\u00e3o, vem:
\\[\\begin{array}{*{20}{l}}{2{x^2} = 5x}& \\Leftrightarrow &{2{x^2} – 5x = 0}\\\\{}& \\Leftrightarrow &{x\\left( {2x – 5} \\right) = 0}\\\\{}& \\Leftrightarrow &{\\begin{array}{*{20}{c}}{x = 0}& \\vee &{2x – 5 = 0}\\end{array}}\\\\{}& \\Leftrightarrow &{\\begin{array}{*{20}{c}}{x = 0}& \\vee &{x = \\frac{5}{2}}\\end{array}}\\end{array}\\]
Como x<\/em> designa um comprimento n\u00e3o nulo, ent\u00e3o \$x > 0\$.
Portanto, o tri\u00e2ngulo e o ret\u00e2ngulo t\u00eam a mesma \u00e1rea para \${x = \\frac{5}{2}}\$.<\/li>\n<\/ol>\n
<< Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"
Enunciado Resolu\u00e7\u00e3o Enunciado Observa a figura. Exprime, em fun\u00e7\u00e3o de x, a \u00e1rea do ret\u00e2ngulo e do tri\u00e2ngulo da figura. Determina o valor de x para o qual o tri\u00e2ngulo e o ret\u00e2ngulo tenham...<\/p>\n","protected":false},"author":1,"featured_media":24859,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,700],"tags":[424,706,198,705],"series":[],"class_list":["post-24856","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-monomios-e-polinomios","tag-8-o-ano","tag-equacao-incompleta-do-2-o-grau","tag-lei-do-anulamento-do-produto","tag-polinomios"],"views":226,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag149-25_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24856","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=24856"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24856\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/24859"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24856"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24856"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24856"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24856"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}