{"id":11467,"date":"2022-07-12T12:40:10","date_gmt":"2022-07-12T07:10:10","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11467"},"modified":"2022-07-12T12:40:14","modified_gmt":"2022-07-12T07:10:14","slug":"prove-that-the-altitude-of-an-equilateral-triangle-of-side-2a-is-sqrt3-a","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/prove-that-the-altitude-of-an-equilateral-triangle-of-side-2a-is-sqrt3-a\/","title":{"rendered":"Prove that the altitude of an equilateral triangle of side 2a is \\(\\sqrt{3} a\\)."},"content":{"rendered":"

Solution :<\/h2>\n

Given<\/strong> : \\(\\triangle\\) ABC, in which each side is of length 2a.\"triangles\"<\/p>\n

To Find<\/strong> : AD (altitude)<\/p>\n

In \\(\\triangle\\) ADB and \\(\\triangle\\) ADC,<\/p>\n

AD = AD\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (common)<\/p>\n

\\(\\angle\\) 1 = \\(\\angle\\) 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(90 each)<\/p>\n

AB = AC\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(given)<\/p>\n

By RHS,<\/p>\n

\\(\\triangle\\) ADB \\(\\cong\\) \\(\\triangle\\)\u00a0 ADC<\/p>\n

So,\u00a0 BD = DC\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(By C.P.C.T)<\/p>\n

\\(\\implies\\) BD = DC = a<\/p>\n

Now, in \\(\\triangle\\) ADB,<\/p>\n

\\({AD}^2\\) + \\({BD}^2\\) = \\({AB}^2\\)<\/p>\n

\\(\\implies\\)\u00a0 \\({AD}^2\\) + \\(a^2\\) = \\((2a)^2\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (By Pythagoras Theorem)<\/p>\n

\\({AD}^2\\) = \\(3a^2\\)\u00a0 \u00a0\\(\\implies\\)\u00a0 \u00a0AD = \\(\\sqrt{3} a\\)<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Given : \\(\\triangle\\) ABC, in which each side is of length 2a. To Find : AD (altitude) In \\(\\triangle\\) ADB and \\(\\triangle\\) ADC, AD = AD\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (common) \\(\\angle\\) 1 = \\(\\angle\\) 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(90 each) AB = AC\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 …<\/p>\n

Prove that the altitude of an equilateral triangle of side 2a is \\(\\sqrt{3} a\\).<\/span> Read More »<\/a><\/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":"\nProve that the altitude of an equilateral triangle of side 2a is \\(\\sqrt{3} a\\). - 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\/prove-that-the-altitude-of-an-equilateral-triangle-of-side-2a-is-sqrt3-a\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Prove that the altitude of an equilateral triangle of side 2a is \\(\\sqrt{3} a\\). - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Given : (triangle) ABC, in which each side is of length 2a. To Find : AD (altitude) In (triangle) ADB and (triangle) ADC, AD = AD\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (common) (angle) 1 = (angle) 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(90 each) AB = AC\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 … Prove that the altitude of an equilateral triangle of side 2a is (sqrt{3} a). 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