{"id":234062,"date":"2025-06-13T17:26:19","date_gmt":"2025-06-13T17:26:19","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=234062"},"modified":"2025-06-13T17:26:23","modified_gmt":"2025-06-13T17:26:23","slug":"el-perimetro-de-un-rectangulo-mide-128-cm-y-la-razon-entre-las-medidas-de-sus-lados-es","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/13\/el-perimetro-de-un-rectangulo-mide-128-cm-y-la-razon-entre-las-medidas-de-sus-lados-es\/","title":{"rendered":"El per\u00edmetro de un rect\u00e1ngulo mide 128 cm y la raz\u00f3n entre las medidas de sus lados es"},"content":{"rendered":"\n<p>El per\u00edmetro de un rect\u00e1ngulo mide 128 cm y la raz\u00f3n entre las medidas de sus lados es 5 a 3. Calcula el \u00e1rea del rect\u00e1ngulo. a) 960 2 b) 96 2 c) 128 2 d) 800 2<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>La respuesta correcta es la&nbsp;<strong>a) 960 cm\u00b2<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explicaci\u00f3n Detallada: C\u00e1lculo del \u00c1rea de un Rect\u00e1ngulo<\/strong><\/h3>\n\n\n\n<p>Para resolver este problema, debemos utilizar la informaci\u00f3n proporcionada \u2014el per\u00edmetro y la raz\u00f3n entre los lados\u2014 para encontrar las dimensiones exactas del rect\u00e1ngulo (su base y su altura) y, posteriormente, calcular su \u00e1rea.<\/p>\n\n\n\n<p><strong>1. Comprender los Datos del Problema:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Per\u00edmetro (P):<\/strong>\u00a0Es la suma de la longitud de todos los lados del rect\u00e1ngulo. La f\u00f3rmula es P = 2 \u00d7 (base + altura). Se nos dice que P = 128 cm.<\/li>\n\n\n\n<li><strong>Raz\u00f3n de los lados:<\/strong>\u00a0La raz\u00f3n es de 5 a 3 (o 5:3). Esto no significa que los lados midan 5 cm y 3 cm, sino que sus longitudes mantienen esa proporci\u00f3n. Podemos representar las longitudes usando una constante de proporcionalidad, que llamaremos\u00a0k.\n<ul class=\"wp-block-list\">\n<li>Lado m\u00e1s largo (base) = 5k<\/li>\n\n\n\n<li>Lado m\u00e1s corto (altura) = 3k<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>2. Plantear la Ecuaci\u00f3n del Per\u00edmetro:<\/strong><\/p>\n\n\n\n<p>Ahora, sustituimos nuestras expresiones para la base y la altura en la f\u00f3rmula del per\u00edmetro:<\/p>\n\n\n\n<p>P = 2 \u00d7 (base + altura)<br>128 = 2 \u00d7 (5k + 3k)<\/p>\n\n\n\n<p><strong>3. Resolver para la Constante de Proporcionalidad (k):<\/strong><\/p>\n\n\n\n<p>El siguiente paso es resolver la ecuaci\u00f3n para encontrar el valor de&nbsp;k, que nos permitir\u00e1 conocer las medidas reales de los lados.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Primero, sumamos los t\u00e9rminos dentro del par\u00e9ntesis:<br>128 = 2 \u00d7 (8k)<\/li>\n\n\n\n<li>Luego, multiplicamos:<br>128 = 16k<\/li>\n\n\n\n<li>Finalmente, despejamos\u00a0k\u00a0dividiendo ambos lados por 16:<br>k = 128 \/ 16<br>k = 8<\/li>\n<\/ul>\n\n\n\n<p><strong>4. Calcular las Dimensiones del Rect\u00e1ngulo:<\/strong><\/p>\n\n\n\n<p>Con el valor de k = 8, ahora podemos encontrar las longitudes reales de la base y la altura:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Base<\/strong>\u00a0= 5k = 5 \u00d7 8 =\u00a0<strong>40 cm<\/strong><\/li>\n\n\n\n<li><strong>Altura<\/strong>\u00a0= 3k = 3 \u00d7 8 =\u00a0<strong>24 cm<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Para verificar, podemos comprobar si el per\u00edmetro es correcto: P = 2 \u00d7 (40 + 24) = 2 \u00d7 64 = 128 cm. La verificaci\u00f3n es exitosa.<\/p>\n\n\n\n<p><strong>5. Calcular el \u00c1rea del Rect\u00e1ngulo:<\/strong><\/p>\n\n\n\n<p>El \u00e1rea (A) de un rect\u00e1ngulo se calcula multiplicando su base por su altura.<\/p>\n\n\n\n<p>A = base \u00d7 altura<br>A = 40 cm \u00d7 24 cm<br><strong>A = 960 cm\u00b2<\/strong><\/p>\n\n\n\n<p>El \u00e1rea del rect\u00e1ngulo es de 960 cent\u00edmetros cuadrados. Por lo tanto, la opci\u00f3n correcta es la&nbsp;<strong>a)<\/strong>.thumb_upthumb_down<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-457.jpeg\" alt=\"\" class=\"wp-image-234063\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>El per\u00edmetro de un rect\u00e1ngulo mide 128 cm y la raz\u00f3n entre las medidas de sus lados es 5 a 3. Calcula el \u00e1rea del rect\u00e1ngulo. a) 960 2 b) 96 2 c) 128 2 d) 800 2 The Correct Answer and Explanation is: La respuesta correcta es la&nbsp;a) 960 cm\u00b2. Explicaci\u00f3n Detallada: C\u00e1lculo del [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-234062","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234062","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=234062"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234062\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=234062"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=234062"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=234062"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}