{"id":133903,"date":"2023-03-11T18:37:07","date_gmt":"2023-03-11T13:07:07","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=133903"},"modified":"2023-03-11T20:15:32","modified_gmt":"2023-03-11T14:45:32","slug":"the-median-of-an-equilateral-triangle-is-increasing-at-the-rate-of-2-v3-cm-s-find-the-rate-at-which-its-side-is-increasing","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/quiz\/the-median-of-an-equilateral-triangle-is-increasing-at-the-rate-of-2-v3-cm-s-find-the-rate-at-which-its-side-is-increasing","title":{"rendered":"The median of an equilateral triangle is increasing at the rate of 2 V3 cm\/s. Find the rate at which its side is increasing."},"content":{"rendered":"

Question: The median of an equilateral triangle is increasing at the rate of 2 V3 cm\/s. Find the rate at which its side is increasing.<\/h2>\n

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The correct answer is –<\/h3>\n
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Let’s denote the side of the equilateral triangle by s, and the median by m.<\/p>\n

Since the triangle is equilateral, the median is also equal to the altitude, and it is known that the altitude of an equilateral triangle is equal to (s*sqrt(3))\/2.<\/p>\n

We want to find ds\/dt, the rate at which the side is increasing.<\/p>\n

We can use the chain rule to relate the rates of change of s and m:<\/p>\n

dm\/dt = dm\/ds * ds\/dt<\/p>\n

We know that dm\/dt = 2sqrt(3) cm\/s, since the median is increasing at a rate of 2<\/em>sqrt(3) cm\/s.<\/p>\n

To find dm\/ds, we can differentiate the formula for the altitude with respect to s:<\/p>\n

m = (s*sqrt(3))\/2 dm\/ds = (sqrt(3))\/2<\/p>\n

Now we can substitute the known values into the chain rule equation to find ds\/dt:<\/p>\n

2*sqrt(3) = (sqrt(3))\/2 * ds\/dt<\/p>\n

Solving for ds\/dt, we get:<\/p>\n

ds\/dt = 4 cm\/s<\/p>\n

Therefore, the rate at which the side of the equilateral triangle is increasing is 4 cm\/s.<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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Question: The median of an equilateral triangle is increasing at the rate of 2 V3 cm\/s. Find the rate at which its side is increasing.   The correct answer is – Let’s denote the side of the equilateral triangle by s, and the median by m. Since the triangle is equilateral, the median is also […]<\/p>\n","protected":false},"author":21842,"featured_media":132233,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12119],"tags":[],"class_list":{"0":"post-133903","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-quiz"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133903","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/users\/21842"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/comments?post=133903"}],"version-history":[{"count":2,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133903\/revisions"}],"predecessor-version":[{"id":133909,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133903\/revisions\/133909"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media\/132233"}],"wp:attachment":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media?parent=133903"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=133903"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=133903"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}