6. If each of two opposite sides of a square is increased by 4 cm and each of other two sides is decreased by 4 cm, we obtain a rectangle of area 84 cm2. What is the perimeter (in cm) of the original square?
A. 40
Let the side of the original square be x cm.According to the question,(x + 4) (x - 4) = 84 ∴ Perimeter of the original square = 4a = 4 x 10 = 40 cmTry our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts Dedicated counsellor for each student Detailed Performance Evaluation view all coursesPage 2Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts Dedicated counsellor for each student Detailed Performance Evaluation view all coursesLet the radius of the two spheres be r and R. As, `"Surface area of the first sphere"/"surface area of the second sphere" = 16/9` `=> (4pi"R"^2)/(4pi"r"^2) = 16/9` `=> (("R")/"r")^2 = 16/9` `=> "R"/"r" = sqrt(16/9)` `=> "R"/"r" = 4/3` .........(i) Now, The ratio of their volumes`= "Volumes of the first sphere"/"Volume of the second sphere"` `=((4/3pi"R"^3))/((4/3pi"r"^3))` `=> ("R"/"r")^3` `=> (4/3)^3` `=>"R"/"r" = 4/3` [Using (i)] `= 64/27` = 64 : 27 Hence, the correct answer is option (a). |