Find the perimeter of a rectangular garden, whose breadth is two-third of its length and area is 486 m².

Correct option is B

Given:

Area of the rectangular garden = 486 m²
Breadth of the garden is two-third of its length.

Formula  Used:

The area of a rectangle is given by: Area = Length × Breadth.
The perimeter of a rectangle is given by: Perimeter = 2(Length + Breadth).

Solution:

Let the length be L and the breadth be B.

$$B = (\frac{2}{3}) × L \\\ \\Area = L × B = 486.\\\ \\L × (\frac{2}{3}) × L = 486\\\ \\(\frac{2}{3})L² = 486\\\ \\L² = \frac{(486 × 3) }{ 2} = 729\\\ \\L = √729 = 27 m$$​​

Now, to find the breadth:
B = (2/3) × 27 = 18 m

To find the perimeter:
Perimeter = 2(L + B) = 2(27 + 18) = 2 × 45 = 90 m
Thus, the perimeter of the rectangular garden is 90 meters.