{"id":11418,"date":"2022-07-08T22:56:35","date_gmt":"2022-07-08T17:26:35","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11418"},"modified":"2022-07-08T22:56:40","modified_gmt":"2022-07-08T17:26:40","slug":"tick-the-correct-answer-and-justify-abc-and-bde-are-two-equilateral-triangles-such-that-d-is-the-mid-point-of-bc-ratio-of-the-areas-of-triangles-abc-and-bde-is-a-2-1-b-1-2-c-4-1-d","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/tick-the-correct-answer-and-justify-abc-and-bde-are-two-equilateral-triangles-such-that-d-is-the-mid-point-of-bc-ratio-of-the-areas-of-triangles-abc-and-bde-is-a-2-1-b-1-2-c-4-1-d\/","title":{"rendered":"Tick the correct answer and justify : ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is   (a) 2 : 1  (b) 1 : 2  (c) 4 : 1  (d) 1 : 4"},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>Since \\(\\triangle\\) ABC and BDE are equilateral triangles, they are equiangular and hence<img decoding=\"async\" loading=\"lazy\" class=\" wp-image-11439 alignright\" src=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-4-8.jpeg?resize=170%2C149&#038;ssl=1\" alt=\"triangle\" width=\"170\" height=\"149\" srcset=\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-4-8.jpeg?resize=300%2C263&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-4-8.jpeg?resize=1024%2C896&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-4-8.jpeg?resize=768%2C672&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-4-8.jpeg?resize=1536%2C1344&amp;ssl=1 1536w, https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-4-8.jpeg?w=1700&amp;ssl=1 1700w\" sizes=\"(max-width: 170px) 100vw, 170px\" data-recalc-dims=\"1\" \/><\/p>\n<p>\\(\\triangle\\) ABC ~ \\(\\triangle\\) BDE<\/p>\n<p>So, \\(area(\\triangle ABC)\\over area(\\triangle BDE)\\) = \\({BC}^2\\over {BD}^2\\)<\/p>\n<p>or\u00a0 \\(area(\\triangle ABC)\\over area(\\triangle BDE)\\) = \\({2BD}^2\\over {AC}^2\\)<\/p>\n<p>\\(\\implies\\)\u00a0 \\(area(\\triangle ABC)\\over area(\\triangle BDE)\\) = \\(4\\over 1\\)<\/p>\n<p>\\(\\therefore\\) <strong>(d) is the correct answer.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : Since \\(\\triangle\\) ABC and BDE are equilateral triangles, they are equiangular and hence \\(\\triangle\\) ABC ~ \\(\\triangle\\) BDE So, \\(area(\\triangle ABC)\\over area(\\triangle BDE)\\) = \\({BC}^2\\over {BD}^2\\) or\u00a0 \\(area(\\triangle ABC)\\over area(\\triangle BDE)\\) = \\({2BD}^2\\over {AC}^2\\) \\(\\implies\\)\u00a0 \\(area(\\triangle ABC)\\over area(\\triangle BDE)\\) = \\(4\\over 1\\) \\(\\therefore\\) (d) is the correct answer.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,912],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Tick the correct answer and justify : ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is  (a) 2 : 1 (b) 1 : 2 (c) 4 : 1 (d) 1 : 4 - Mathemerize<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/tick-the-correct-answer-and-justify-abc-and-bde-are-two-equilateral-triangles-such-that-d-is-the-mid-point-of-bc-ratio-of-the-areas-of-triangles-abc-and-bde-is-a-2-1-b-1-2-c-4-1-d\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Tick the correct answer and justify : ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is  (a) 2 : 1 (b) 1 : 2 (c) 4 : 1 (d) 1 : 4 - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Since (triangle) ABC and BDE are equilateral triangles, they are equiangular and hence (triangle) ABC ~ (triangle) BDE So, (area(triangle ABC)over area(triangle BDE)) = ({BC}^2over {BD}^2) or\u00a0 (area(triangle ABC)over area(triangle BDE)) = ({2BD}^2over {AC}^2) (implies)\u00a0 (area(triangle ABC)over area(triangle BDE)) = (4over 1) (therefore) (d) is the correct answer.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/tick-the-correct-answer-and-justify-abc-and-bde-are-two-equilateral-triangles-such-that-d-is-the-mid-point-of-bc-ratio-of-the-areas-of-triangles-abc-and-bde-is-a-2-1-b-1-2-c-4-1-d\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2022-07-08T17:26:35+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-07-08T17:26:40+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-4-8-300x263.jpeg\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/tick-the-correct-answer-and-justify-abc-and-bde-are-two-equilateral-triangles-such-that-d-is-the-mid-point-of-bc-ratio-of-the-areas-of-triangles-abc-and-bde-is-a-2-1-b-1-2-c-4-1-d\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/tick-the-correct-answer-and-justify-abc-and-bde-are-two-equilateral-triangles-such-that-d-is-the-mid-point-of-bc-ratio-of-the-areas-of-triangles-abc-and-bde-is-a-2-1-b-1-2-c-4-1-d\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Tick the correct answer and justify : ABC and BDE are two equilateral triangles such that D is the mid-point of BC. 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Ratio of the areas of triangles ABC and BDE is  (a) 2 : 1 (b) 1 : 2 (c) 4 : 1 (d) 1 : 4 - Mathemerize","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/tick-the-correct-answer-and-justify-abc-and-bde-are-two-equilateral-triangles-such-that-d-is-the-mid-point-of-bc-ratio-of-the-areas-of-triangles-abc-and-bde-is-a-2-1-b-1-2-c-4-1-d\/","og_locale":"en_US","og_type":"article","og_title":"Tick the correct answer and justify : ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is  (a) 2 : 1 (b) 1 : 2 (c) 4 : 1 (d) 1 : 4 - Mathemerize","og_description":"Solution : Since (triangle) ABC and BDE are equilateral triangles, they are equiangular and hence (triangle) ABC ~ (triangle) BDE So, (area(triangle ABC)over area(triangle BDE)) = ({BC}^2over {BD}^2) or\u00a0 (area(triangle ABC)over area(triangle BDE)) = ({2BD}^2over {AC}^2) (implies)\u00a0 (area(triangle ABC)over area(triangle BDE)) = (4over 1) (therefore) (d) is the correct answer.","og_url":"https:\/\/mathemerize.com\/tick-the-correct-answer-and-justify-abc-and-bde-are-two-equilateral-triangles-such-that-d-is-the-mid-point-of-bc-ratio-of-the-areas-of-triangles-abc-and-bde-is-a-2-1-b-1-2-c-4-1-d\/","og_site_name":"Mathemerize","article_published_time":"2022-07-08T17:26:35+00:00","article_modified_time":"2022-07-08T17:26:40+00:00","og_image":[{"url":"https:\/\/mathemerize.com\/wp-content\/uploads\/2022\/07\/similartriangles6-4-8-300x263.jpeg"}],"author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/tick-the-correct-answer-and-justify-abc-and-bde-are-two-equilateral-triangles-such-that-d-is-the-mid-point-of-bc-ratio-of-the-areas-of-triangles-abc-and-bde-is-a-2-1-b-1-2-c-4-1-d\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/tick-the-correct-answer-and-justify-abc-and-bde-are-two-equilateral-triangles-such-that-d-is-the-mid-point-of-bc-ratio-of-the-areas-of-triangles-abc-and-bde-is-a-2-1-b-1-2-c-4-1-d\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"Tick the correct answer and justify : ABC and BDE are two equilateral triangles such that D is the mid-point of BC. 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