Question
The perimeter of a rectangle of length 2(x + 2) cm and
breadth 2(x + 4) cm is double the perimeter of a square of area 256 cm². Find the area of the rectangle.Solution
Area of square = 256 cm²  Side of square = √256 = 16 cm  Perimeter of square = 16 × 4 = 64 cm  So, perimeter of rectangle = 2 × 64 = 128 cm  ⇒ 2(2(x + 2) + 2(x + 4)) = 128  ⇒ 4x + 12 = 64  ⇒ 4x = 52  ⇒ x = 13  So, length of rectangle = 2(13 + 2) = 30 cm  And, breadth of rectangle = 2(13 + 4) = 34 cm  Therefore, area of rectangle = 30 × 34 = 1020 cm²
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