Solve the following mathematical problems:

A lawn is in the form of a rectangle having its sides in the ratio 2: 3. The area of the lawn is 1/6 hectares. Find the length and breadth of the lawn. (Geometry (Rectangle))

dsuc.created: 2 years ago | dsuc.updated: 2 years ago

dsuc.updated: 2 years ago

প্রশ্নে বলা হচ্ছে, আয়তাকৃতির একটি নলের দৈর্ঘ্য ও প্রস্থের অনুপাত 2 : 3, নলটির ক্ষেত্রফল $\frac{1}{6}$ হেক্টর। নলটির দৈর্ঘ্য এবং প্রস্থ কত?

Let, the length of the lawn is 2x meter

& the breadth of the lawn is 3x meter

$∴ A r e a = (2 x \times 3 x) m^{2} = 6 x^{2} m^{2} W e k n o w, 1 h e c t o r = 10, 000 m^{2} ∴ \frac{1}{6} h e c t o r = \frac{10000}{6} m^{2} A c c o r d i n g t o q u e s t i o n 6 x^{2} = \frac{10000}{6} \Rightarrow x^{2} = \frac{10000}{6 \times 6} \Rightarrow x = \sqrt{{(\frac{100}{6})}^{2}} ∴ x = \frac{100}{6} = \frac{50}{3} ∴ T h e l e n g t h o f t h e l a w n = 2 x = (2 \times \frac{50}{3}) = \frac{100}{3} m e t e r o r 33.33 m e t e r & t h e b r e a d t h o f t h e l a w n = 3 x = (3 \times \frac{50}{3}) = 50 m e t e r$