Mathematics
The length of a rectangular garden is 12 m more than its breadth. The numerical value of its area is equal to 4 times the numerical value of its perimeter. Find the dimensions of the garden.
Answer
Let breadth of rectangular garden = x meters,
∴ Length = (x + 12) meters.
Area of garden = length × breadth = x(x + 12) m2
Perimeter of garden = 2(l + b)
= 2[(x + 12) + x]
= 2[2x + 12] = (4x + 24) meters.
According to question,
⇒ Area of garden = 4 × Perimeter of garden
⇒ x(x + 12) = 4 × (4x + 24)
⇒ x2 + 12x = 16x + 96
⇒ x2 + 12x - 16x - 96 = 0
⇒ x2 - 4x - 96 = 0
⇒ x2 - 12x + 8x - 96 = 0
⇒ x(x - 12) + 8(x - 12) = 0
⇒ (x + 8)(x - 12) = 0
⇒ x + 8 = 0 or x - 12 = 0
⇒ x = -8 or x = 12.
Since, breadth cannot be negative.
∴ x ≠ -8.
Breadth = x = 12 m and Length = (x + 12) = (12 + 12) = 24 m.
Hence, length and breadth of garden are 24 m and 12 m respectively.
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