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5.
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
Let 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).