Subject
Quantitative Aptitude
Topic
Areas & Volumes
The length of a rectangle is thrice its breadth, and its perimeter is 104 meters. What is its area?
The length of a rectangle is thrice its breadth, and its perimeter is 104 meters. What is its area?
ক)
507 sq. m.খ)
624 sq. m.গ)
416 sq. m.ঘ)
312 sq. m.Explanation
ধরি, আয়তক্ষেত্রটির প্রস্থ হল P মিটার। প্রশ্ন অনুযায়ী, আয়তক্ষেত্রটির দৈর্ঘ্য তার প্রস্থের তিনগুণ। সুতরাং, দৈর্ঘ্য হবে 3P মিটার। আয়তক্ষেত্রের পরিসীমা সূত্র হল 2×(দৈর্ঘ্য+প্রস্থ)। প্রশ্নমতে, পরিসীমা হল 104 মিটার। তাহলে, 2×(3P+P)=104 বা, 2×(4P)=104 বা, 8P=104 বা, P=13 মিটার সুতরাং, আয়তক্ষেত্রটির প্রস্থ হল 13 মিটার। এবং দৈর্ঘ্য হল 3×13=39 মিটার। ক্ষেত্রফল = 39×13 বর্গমিটার = 507 বর্গমিটার অতএব, আয়তক্ষেত্রটির ক্ষেত্রফল হল 507 বর্গমিটার।Related questions
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