Complete the following: A rectangle has sides 2x + y + 8 (top), 4x - y (bottom), 2y (left) and x + 4 (right). Find the values of x and y. Find its perimeter and area.

Answer: \(x = 12\), \(y = 8\); perimeter = 112 units, area = 640 sq. units

Opposite sides of a rectangle are equal.

Upper = lower: \(2x + y + 8 = 4x - y\), so \(2x - 2y = 8\), i.e. \(x - y = 4\) ... (I)

Left = right: \(2y = x + 4\), so \(x - 2y = -4\) ... (II)

Subtract (II) from (I): \(y = 8\). Then \(x = 4 + 8 = 12\).

Length \(= 2x + y + 8 = 24 + 8 + 8 = 40\) (check: \(4x - y = 48 - 8 = 40\)).
Breadth \(= 2y = 16\) (check: \(x + 4 = 16\)).

Perimeter \(= 2(40 + 16) = 112\) units.
Area \(= 40 \times 16 = 640\) sq. units.