Mathematics
The length of a rectangle is 4 cm more than its breadth. If the area of the rectangle is 96 cm2, then the perimeter of the rectangle is :
36 cm
40 cm
44 cm
48 cm
Answer
Let the breadth and length of a rectangle be x cm and (x + 4) cm.
Given,
Area of rectangle = 96 cm2.
⇒ x(x + 4) = 96
⇒ x2 + 4x = 96
⇒ x2 + 4x - 96 = 0
⇒ x2 - 8x + 12x - 96 = 0
⇒ x(x - 8) + 12(x - 8) = 0
⇒ (x + 12)(x - 8) = 0
⇒ (x + 12) = 0 or (x - 8) = 0 [Using zero-product rule]
⇒ x = -12 or x = 8
Since length and breadth cannot be negative, thus Breadth = x = 8 cm.
Length = x + 4 = 8 + 4 = 12 cm
Perimeter of the rectangle = 2(l + b)
= 2(12 + 8)
= 2(20)
= 40 cm.
Hence, option 2 is the correct option.
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