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