{"id":89237,"date":"2025-06-01T09:59:34","date_gmt":"2025-06-01T09:59:34","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=89237"},"modified":"2025-06-01T09:59:34","modified_gmt":"2025-06-01T09:59:34","slug":"the-width-of-a-rectangle-is-4x-which-is-only-25-of-its-length-what-a","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-width-of-a-rectangle-is-4x-which-is-only-25-of-its-length-what-a\/","title":{"rendered":"The width of a rectangle is 4x which is only 25% of its length. What a"},"content":{"rendered":"

The width of a rectangle is 4x which is only 25% of its length. What are the area and the perimeter of the rectangle respectively ?<\/p>\n

[amp_mcq option1=”16x\u00b2 squnit and 16x unit” option2=”20x\u00b2 squnit and 40x unit” option3=”32x\u00b2 squnit and 64x unit” option4=”64x\u00b2 squnit and 40x unit” correct=”option4″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2009<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nLet the width of the rectangle be w and the length be l.
\nWe are given the width: w = 4x.
\nWe are told that the width is 25% of its length.
\nw = 25% of l
\nw = 0.25 * l
\nSubstitute the value of w:
\n4x = 0.25 * l
\nTo find the length l, divide by 0.25:
\nl = 4x \/ 0.25
\nl = 4x \/ (1\/4)
\nl = 4x * 4
\nl = 16x<\/p>\n

So, the length of the rectangle is 16x and the width is 4x.<\/p>\n

Area of the rectangle = length * width
\nArea = l * w = (16x) * (4x) = 16 * 4 * x * x = 64x\u00b2 sq units.<\/p>\n

Perimeter of the rectangle = 2 * (length + width)
\nPerimeter = 2 * (l + w) = 2 * (16x + 4x) = 2 * (20x) = 40x units.<\/p>\n

The area is 64x\u00b2 sq units and the perimeter is 40x units.
\n<\/section>\n

\nThe problem requires calculating the area and perimeter of a rectangle given its width and a relationship between its width and length. The key steps are converting the percentage relationship into an equation, solving for the length, and then applying the standard formulas for the area and perimeter of a rectangle.
\n<\/section>\n
\nUnderstanding that 25% is equivalent to the fraction 1\/4 simplifies the calculation of the length. Area is always in square units, and perimeter is in linear units. The variable ‘x’ is treated algebraically throughout the calculations.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

The width of a rectangle is 4x which is only 25% of its length. What are the area and the perimeter of the rectangle respectively ? [amp_mcq option1=”16x\u00b2 squnit and 16x unit” option2=”20x\u00b2 squnit and 40x unit” option3=”32x\u00b2 squnit and 64x unit” option4=”64x\u00b2 squnit and 40x unit” correct=”option4″] This question was previously asked in UPSC … <\/p>\n

Detailed SolutionThe width of a rectangle is 4x which is only 25% of its length. What a<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1085],"tags":[1462,1102],"class_list":["post-89237","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1462","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nThe width of a rectangle is 4x which is only 25% of its length. What a<\/title>\n<meta name=\"description\" content=\"Let the width of the rectangle be w and the length be l. We are given the width: w = 4x. We are told that the width is 25% of its length. w = 25% of l w = 0.25 * l Substitute the value of w: 4x = 0.25 * l To find the length l, divide by 0.25: l = 4x \/ 0.25 l = 4x \/ (1\/4) l = 4x * 4 l = 16x So, the length of the rectangle is 16x and the width is 4x. Area of the rectangle = length * width Area = l * w = (16x) * (4x) = 16 * 4 * x * x = 64x\u00b2 sq units. Perimeter of the rectangle = 2 * (length + width) Perimeter = 2 * (l + w) = 2 * (16x + 4x) = 2 * (20x) = 40x units. The area is 64x\u00b2 sq units and the perimeter is 40x units. The problem requires calculating the area and perimeter of a rectangle given its width and a relationship between its width and length. The key steps are converting the percentage relationship into an equation, solving for the length, and then applying the standard formulas for the area and perimeter of a rectangle.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/the-width-of-a-rectangle-is-4x-which-is-only-25-of-its-length-what-a\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The width of a rectangle is 4x which is only 25% of its length. What a\" \/>\n<meta property=\"og:description\" content=\"Let the width of the rectangle be w and the length be l. We are given the width: w = 4x. We are told that the width is 25% of its length. w = 25% of l w = 0.25 * l Substitute the value of w: 4x = 0.25 * l To find the length l, divide by 0.25: l = 4x \/ 0.25 l = 4x \/ (1\/4) l = 4x * 4 l = 16x So, the length of the rectangle is 16x and the width is 4x. Area of the rectangle = length * width Area = l * w = (16x) * (4x) = 16 * 4 * x * x = 64x\u00b2 sq units. Perimeter of the rectangle = 2 * (length + width) Perimeter = 2 * (l + w) = 2 * (16x + 4x) = 2 * (20x) = 40x units. The area is 64x\u00b2 sq units and the perimeter is 40x units. The problem requires calculating the area and perimeter of a rectangle given its width and a relationship between its width and length. The key steps are converting the percentage relationship into an equation, solving for the length, and then applying the standard formulas for the area and perimeter of a rectangle.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-width-of-a-rectangle-is-4x-which-is-only-25-of-its-length-what-a\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T09:59:34+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"The width of a rectangle is 4x which is only 25% of its length. What a","description":"Let the width of the rectangle be w and the length be l. We are given the width: w = 4x. We are told that the width is 25% of its length. w = 25% of l w = 0.25 * l Substitute the value of w: 4x = 0.25 * l To find the length l, divide by 0.25: l = 4x \/ 0.25 l = 4x \/ (1\/4) l = 4x * 4 l = 16x So, the length of the rectangle is 16x and the width is 4x. Area of the rectangle = length * width Area = l * w = (16x) * (4x) = 16 * 4 * x * x = 64x\u00b2 sq units. Perimeter of the rectangle = 2 * (length + width) Perimeter = 2 * (l + w) = 2 * (16x + 4x) = 2 * (20x) = 40x units. The area is 64x\u00b2 sq units and the perimeter is 40x units. The problem requires calculating the area and perimeter of a rectangle given its width and a relationship between its width and length. The key steps are converting the percentage relationship into an equation, solving for the length, and then applying the standard formulas for the area and perimeter of a rectangle.","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:\/\/exam.pscnotes.com\/mcq\/the-width-of-a-rectangle-is-4x-which-is-only-25-of-its-length-what-a\/","og_locale":"en_US","og_type":"article","og_title":"The width of a rectangle is 4x which is only 25% of its length. What a","og_description":"Let the width of the rectangle be w and the length be l. We are given the width: w = 4x. We are told that the width is 25% of its length. w = 25% of l w = 0.25 * l Substitute the value of w: 4x = 0.25 * l To find the length l, divide by 0.25: l = 4x \/ 0.25 l = 4x \/ (1\/4) l = 4x * 4 l = 16x So, the length of the rectangle is 16x and the width is 4x. Area of the rectangle = length * width Area = l * w = (16x) * (4x) = 16 * 4 * x * x = 64x\u00b2 sq units. Perimeter of the rectangle = 2 * (length + width) Perimeter = 2 * (l + w) = 2 * (16x + 4x) = 2 * (20x) = 40x units. The area is 64x\u00b2 sq units and the perimeter is 40x units. The problem requires calculating the area and perimeter of a rectangle given its width and a relationship between its width and length. The key steps are converting the percentage relationship into an equation, solving for the length, and then applying the standard formulas for the area and perimeter of a rectangle.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-width-of-a-rectangle-is-4x-which-is-only-25-of-its-length-what-a\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T09:59:34+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-width-of-a-rectangle-is-4x-which-is-only-25-of-its-length-what-a\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-width-of-a-rectangle-is-4x-which-is-only-25-of-its-length-what-a\/","name":"The width of a rectangle is 4x which is only 25% of its length. What a","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T09:59:34+00:00","dateModified":"2025-06-01T09:59:34+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Let the width of the rectangle be w and the length be l. We are given the width: w = 4x. We are told that the width is 25% of its length. w = 25% of l w = 0.25 * l Substitute the value of w: 4x = 0.25 * l To find the length l, divide by 0.25: l = 4x \/ 0.25 l = 4x \/ (1\/4) l = 4x * 4 l = 16x So, the length of the rectangle is 16x and the width is 4x. Area of the rectangle = length * width Area = l * w = (16x) * (4x) = 16 * 4 * x * x = 64x\u00b2 sq units. Perimeter of the rectangle = 2 * (length + width) Perimeter = 2 * (l + w) = 2 * (16x + 4x) = 2 * (20x) = 40x units. The area is 64x\u00b2 sq units and the perimeter is 40x units. The problem requires calculating the area and perimeter of a rectangle given its width and a relationship between its width and length. The key steps are converting the percentage relationship into an equation, solving for the length, and then applying the standard formulas for the area and perimeter of a rectangle.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/the-width-of-a-rectangle-is-4x-which-is-only-25-of-its-length-what-a\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/the-width-of-a-rectangle-is-4x-which-is-only-25-of-its-length-what-a\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-width-of-a-rectangle-is-4x-which-is-only-25-of-its-length-what-a\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CAPF","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-capf\/"},{"@type":"ListItem","position":3,"name":"The width of a rectangle is 4x which is only 25% of its length. 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