The area of a rectangle is 192 cm2 and its perimeter is 56 cm. Find the dimensions of the rectangle.

Given: Area of rectangle = 192 cm2


Perimeter of rectangle = 56 cm



Let,


Length be l cm


And, breadth be b cm


Now,


Area of rectangle = Length × Breadth


192 cm2 = l cm × b cm



Perimeter of rectangle = 2(length + breadth)


56 cm = 2(l cm + b cm)


Now, substituting the value of l in this we get,






28b = 192 + b2


b2- 28b + 192 = 0


b2- 16 b – 12 b + 192 = 0


b(b - 16 ) – 12(b - 16 ) = 0


(b - 12 ) (b - 16 ) = 0


This gives us two equations,


i. b – 12 = 0


b = 12


ii. b – 16 = 0


b = 16


Let b = 12 cm



Hence,


Length = 16 cm


Breadth = 12 cm


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