Explanation:
Area of square = 36cm^2
Area of each rectangle = 1 1/3 of 36cm^2
= 4/3 × 36 = 4 × 12 = 48cm^2.
By inspection one can see that the magnitude of the dimensions of the square is common for all the rectangle as their width (base).
But Area of a square = side squared (s^2)
so we have: 36 = s^2
taking the square root of both sides:
we have:. s = 6cm.
hence each rectangle has a width of 6cm.
But Area of a rectangle = L × W
48 = L × 6
48 = 6L
L = 8cm
hence each rectangle has a length of 8 cm.
perimeter of outward dimensions of each rectangle = L + L + W = 2L + W
since the rectangles are four in number;
the perimeter of the area shaped pattern
= 4(2L + W)
= 4(2(8) + 6)
= 4(24) = 96cm.