{"id":18552,"date":"2025-06-13T07:28:41","date_gmt":"2025-06-13T07:28:41","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=18552"},"modified":"2025-06-13T07:28:43","modified_gmt":"2025-06-13T07:28:43","slug":"length-4-x-width-x-height-x2-1-what-is-the-base-area-of-box-3","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/length-4-x-width-x-height-x2-1-what-is-the-base-area-of-box-3\/","title":{"rendered":"Length = 4 + x Width = x Height = x2 + 1 What is the base area of Box 3"},"content":{"rendered":"\n<p>Length = 4 + x Width = x Height = x2 + 1 What is the base area of Box 3?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p>To find the <strong>base area of Box 3<\/strong>, we are given the following:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Length<\/strong> = 4+x4 + x<\/li>\n\n\n\n<li><strong>Width<\/strong> = xx<\/li>\n\n\n\n<li><strong>Height<\/strong> = x2+1x^2 + 1<\/li>\n<\/ul>\n\n\n\n<p>However, the question only asks for the <strong>base area<\/strong>, which is the area of the <strong>rectangle<\/strong> formed by the <strong>length and width<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 1: Formula for Base Area<\/strong><\/h3>\n\n\n\n<p>The <strong>base area (A)<\/strong> of a rectangular box is calculated by: A=Length\u00d7WidthA = \\text{Length} \\times \\text{Width}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 2: Plug in the Given Expressions<\/strong><\/h3>\n\n\n\n<p>Using the expressions provided: A=(4+x)\u00d7xA = (4 + x) \\times x<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 3: Simplify the Expression<\/strong><\/h3>\n\n\n\n<p>Now multiply the binomial: A=x(4+x)=4x+x2A = x(4 + x) = 4x + x^2<\/p>\n\n\n\n<p>So, the <strong>base area of Box 3 is<\/strong>: x2+4x\\boxed{x^2 + 4x}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>300-Word Explanation:<\/strong><\/h3>\n\n\n\n<p>To determine the base area of a rectangular box, you only need the <strong>length<\/strong> and <strong>width<\/strong> measurements, because the base is simply a flat rectangle. In this problem, we are given expressions rather than specific numbers:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>length<\/strong> of the box is 4+x4 + x,<\/li>\n\n\n\n<li>The <strong>width<\/strong> is xx,<\/li>\n\n\n\n<li>And while the <strong>height<\/strong> is given as x2+1x^2 + 1, it is <strong>not relevant<\/strong> for finding the base area.<\/li>\n<\/ul>\n\n\n\n<p>The base area of any rectangle is calculated by multiplying the <strong>length<\/strong> by the <strong>width<\/strong>. That\u2019s why we take (4+x)\u00d7x(4 + x) \\times x. This is an example of using the <strong>distributive property<\/strong> in algebra: multiplying a monomial by a binomial.<\/p>\n\n\n\n<p>So, (4+x)\u00d7x=4x+x2(4 + x) \\times x = 4x + x^2<\/p>\n\n\n\n<p>This result, x2+4xx^2 + 4x, is an <strong>algebraic expression<\/strong> that represents the area of the base in terms of the variable xx. It means that for any value of xx, you can plug it into this expression to find the specific area. For example, if x=2x = 2, then the base area would be: 22+4(2)=4+8=122^2 + 4(2) = 4 + 8 = 12<\/p>\n\n\n\n<p>In conclusion, the base area is <strong>not a fixed number<\/strong> but an expression that depends on xx. The correct answer is: x2+4x\\boxed{x^2 + 4x}<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Length = 4 + x Width = x Height = x2 + 1 What is the base area of Box 3? The correct answer and explanation is: To find the base area of Box 3, we are given the following: However, the question only asks for the base area, which is the area of the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-18552","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18552","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=18552"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18552\/revisions"}],"predecessor-version":[{"id":18553,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18552\/revisions\/18553"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=18552"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=18552"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=18552"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}