An equilateral triangle has a perimeter of 15×3 33×5 feet. what is the length of each side?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To find the length of each side of an equilateral triangle with a given perimeter, we first need to understand the properties of equilateral triangles. An equilateral triangle has three equal sides, meaning that each side is of the same length.<\/p>\n\n\n\n The perimeter ( P ) of an equilateral triangle can be expressed mathematically as:<\/p>\n\n\n\n [ where ( s ) is the length of one side. In this case, the problem states that the perimeter is ( 15x^3 + 33x^5 ) feet.<\/p>\n\n\n\n From the perimeter formula, we can set up the equation:<\/p>\n\n\n\n [ To find ( s ), we need to isolate it on one side of the equation. We can do this by dividing both sides by 3:<\/p>\n\n\n\n [ Next, we simplify the right side:<\/p>\n\n\n\n [ Thus, the length of each side of the equilateral triangle is:<\/p>\n\n\n\n [ This means that each side of the triangle is a polynomial expression in terms of ( x ). The term ( 5x^3 ) indicates that there is a cubic relationship with ( x ), while ( 11x^5 ) indicates a quintic relationship. The total length of each side combines these two expressions, reflecting the contributions of both terms.<\/p>\n\n\n\n By factoring the expression, we can see that ( x ) plays a significant role in determining the specific length of the sides. If ( x ) is given a particular numerical value, we can further evaluate the length of each side in feet.<\/p>\n","protected":false},"excerpt":{"rendered":" An equilateral triangle has a perimeter of 15×3 33×5 feet. what is the length of each side? The Correct Answer and Explanation is : To find the length of each side of an equilateral triangle with a given perimeter, we first need to understand the properties of equilateral triangles. An equilateral triangle has three equal […]<\/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-147559","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/147559","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=147559"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/147559\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=147559"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=147559"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=147559"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Understand the Perimeter<\/h3>\n\n\n\n
P = 3s
]<\/p>\n\n\n\nStep 2: Set Up the Equation<\/h3>\n\n\n\n
3s = 15x^3 + 33x^5
]<\/p>\n\n\n\nStep 3: Solve for ( s )<\/h3>\n\n\n\n
s = \\frac{15x^3 + 33x^5}{3}
]<\/p>\n\n\n\nStep 4: Simplify the Expression<\/h3>\n\n\n\n
s = \\frac{15x^3}{3} + \\frac{33x^5}{3} = 5x^3 + 11x^5
]<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n
s = 5x^3 + 11x^5 \\text{ feet}
]<\/p>\n\n\n\nExplanation<\/h3>\n\n\n\n